VALUATION METHODS AND THE USE OF COMPUTERS IN THE
ACQUISITION ANALYSIS OF PRIVATELY OWNED FIRMS
by
George Alvarez-Correa
S. B., Massachusetts Institute of Technology
(1971)
and
Sergio Brosio
Dott., University of Torino
( 1964)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF MASTER OF SCIENCE IN MANAGEMENT
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
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1972
December,
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Signature
of Authors
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Archives
-2-
VALUATION METHODS AND THE USE OF COMPUTERS IN THE
ACQUISITION ANALYSIS OF PRIVATELY OWNED FIRMS
George Alvarez-Correa
Sergio Brosio
Submitted to the Alfred P. Sloan School of Management on
December 22, 1972, in partial fulfillment of the requirements for the
degree of Master of Science in Management
ABSTRACT
The main economic justification for mergers and acquisitions
is the creation of an entity whose market value is greater than the sum
of the values of the merging firms considered as separate entities.
Among the problems facing a corporation in evaluating a merger candidate is that of determining the price to be offered. The problem is
compoundedwhen the firm to be acquired is a privately-held corporation whose shares are not traded in the market.
This thesis suggests that the process of premerger valuation
be structured in such a way as to allow explicit and separate valuation
of the fair market value of the firm to be acquired, and of the syner-
gistic benefits expected to accrue as a result of the merger. The analysis
is limited to those benefits which are financial in nature.
In the course of the thesis, we first illustrate some of the
methods and techniques that are available for evaluating non-public
firms with explicit consideration given to the uncertainties involved.
We then examine the financial impact of the issues in price negotiations, such as media of exchange, type of transaction, schedule and
forms of payment, and related tax implications. We develop an appli-
cation of goal programming to the problem of structuring the securities
package to be used as payment. Drawing upon this background of
methods and techniques, we then present a framework of analysis and
provide practical guidelines to establish a maximum price to be paid
for an acquisition.
-3-
Last, we investigate the general use of computers in support
of merger analysis. We first present a survey of computer programs
which have appeared in the literature or which we have obtained from
other sources. We conclude by presenting and illustrating the use of
an interactive program which was developed to aid the decision-maker
in structuring a transaction package consistent with several of his
operational and financial goals.
Thesis Supervisor:
Stewart C. Myers
Title:
Associate Professor
of Finance
-4ACKNOWLEDGEMENTS
There are many people who have willingly helped us during the
course of this thesis from its inception through its natural conclusion:
we wish to thank them all.
We would like to single out our appreciation for the assistance,
encouragement and significant contributions to our work provided by
Professor Stewart C. Myers, our thesis advisor.
We equally thank
Professor David Ness, our co-advisor, for his valuable suggestions
and comments, particularly in the computer-related
part of our work.
We also wish to thank Professors Samuel Hayes III, Colin Blaydon and
John Hammond of the Harvard Business School for their helpful comments and assistance.
We further wish to thank Miss Helga Just for her assistance in
typing part of the initial draft, and Miss Rita Asare, who exhibited
skill and patience in typing the many drafts of this thesis and was res ponsible for coordinating and producing the final copy.
Lastly, we wish to express our deepest gratitude to our families who made it possible for us to devote time and energy to this work.
Thank you, Magda, for sharing much of our burden and for your re-
assuring smile.
Despite the aid of all these people, we alone bear full respon-
sibility for the material presented in this paper and for any errors or
shortcomings which remain.
-5TABLE OF CONTENTS
Chapter
Page
Title
Section
I
Chapter II
Chapter III
Introduction
14
Fair Market Value: Valuation Methods
20
A.
Net Assets Valuation Approach
23
B.
Market Valuation Approach
26
C.
Valuation of Potential Cash Flows
29
1.
Discounted Cash Flow Technique
30
1. 1
Cash Flow Projections
30
1.2
Terminal Value
32
1.3
Discount Rate
37
1.4
Present Value of Cash Flows
43
2.
Certainty Equivalent Technique
44
3.
Probability Distribution Analysis
47
Value to the Buyer: Valuation Methods
52
A.
Total Cash Flow Analysis
54
B.
Synergism:
A Framework
of Analysis
59
1.
Benefits
61
2.
Costs
64
3.
Discount Rates
66
4.
3. 1
Determination
of RV2
67
3. 2
Determination
of ARV3
68
Price of the Acquisition
69
-6TABLE OF CONTENTS (Cont.)
Title
Section
Chapter IV
Page
Other Factors in Determining the Acquisition
Price
A.
Chapter V
Earnings Per Share
73
1.
The Chain Letter Effect
73
2.
Short-Term Dilution
75
3.
Long-Term Dilution
77
B.
R.O.I.
88
C.
Diversification
92
Forms of Payment
A.
Chapter VI
72
Type of Transaction:
104
Purchase
and
R eorganization
105
1.
Purchase
106
2.
Reorganization
107
B.
Tax Implications in Merger Negotiations
110
C.
The Contingent Contract
113
1.
Contract Types
114
2.
Advantages and Disadvantages
116
Acquisition Analysis: A Procedural Framework
119
-7 -
TABLE OF CONTENTS (Cont.)
Title
Section
Chapter VII
Page
Structuring the Merger Package
129
A.
The Nature of Goal Programming
131
B.
Goal Programming Applied to Merger
C.
Packaging Analysis
137
1.
Transaction Constraint
140
2.
Short-Term EPS Dilution
Constraint
141
3.
Ownership Goal
143
4.
Solvency Goal
144
5.
Earnings -Per-Share Growth Goal
145
6.
Net Working Capital Goal
148
7.
Objective Function
149
Linearization of Penalty Functions
158
1.
EPS Dilution Penalty Function
158
2.
Ownership Penalty Function
162
3.
Solvency Penalty Function
168
Chapter VIII The Use of Computers in Merger Analysis
A.
173
Introduction
173
1.
Characteristics of Merger Analysis
174
2.
Advantages and Disadvantages
Computer Analysis
of
175
-8TABLE OF CONTENTS (Cont.)
Title
Section
3.
Page
Characteristics
and Differences
of Available Programs
B.
The Available Programs
177
179
1.
The MCKINSEY Program
179
2.
The QUICKSCAN Program
191
3.
MERGERESTIMATOR
194
4.
The REALSCAN Program
203
5.
The PROSIM Program
212
6.
The PRODEP Program
221
7.
The Corning-Glass Works (CGW)
8.
9.
Program
228
The COMMAND Program
232
8. 1
PASTFLOW
232
8.2
CASHPLAN
233
8.3
EDIT
233
8.4
PRODPLAN
233
8.5
MERGE
234
8.6
TARGET
234
The RAYTHEON Program
236
-9-
TABLE OF CONTENTS (Cont.)
Title
Section
C.
The Relationship of the Programs to
Our Framework of Analysis
1.
2.
Comparison of Programs
The FUSION Program
A.
240
Adjustements to the Maximum Price
Before Taxes
Chapter IX
239
Determination of the Acquisition's
Fair Market Value
3.
239
Projection of the Acquisition's
Future Cash Flows
D.
Page
241
242
243
A Note on Time -Sharing A cquis ition
A nalysis
244
B.
Introduction to FUSION
246
C.
Using FUSION
248
D.
Evaluation of FUSION
251
Chapter X
Summary and Conclusion
254
Appendix A
Adjusted P/E Valuation Method
258
Appendix B
Factors Affecting the P/E Ratio
271
-10TABLE OF CONTENTS (Cont.)
Title
Section
Appendix C
Determination of a Discount Rate:
Page
The Cost
of Capital
275
Appendix D
Risk-Equivalent Rate of Return
283
Appendix E
Alphabetical List of Acronyms Used
293
Appendix F
The QUICKSCAN II Program
295
Appendix G
A Sample Session Using FUSION
304
Bibliography
345
-11LIST OF TABLES
Title
Ta ble No.
Page
2-1
Terminal Value
34
3-1
Applicability of Discount Rates
69
8-1
Exhibit 1 - Current and Projected Data
181
8-2
Exhibit 2 - Financial Picture of Superior Tree
Before Acquisitions
8-3
182
Exhibit 3 - Superior Acquiring a Typical Home
Building Company in 1969, 1970, and 1971
184
8-4
Exhibit 4 - Financial Projections for Deluxe Homes
184
8-5
Exhibit 5 - Superior Tree Acquiring Deluxe Homes
in 1969 - Share Data
8-6
186
Exhibit 6 - Superior Tree Acquiring Deluxe Homes
in 1969 - Financial Statements
188
8-7
Sample Output Page from QUICKSCAN
193
8-8
Sample Output of MERGERESTIMATOR
198
8-9
Sample Output of MERGERESTIMATOR
199
8-10
Sample Output of MERGERESTIMATOR
201
8-11
Sample Session with REALSCAN
206
8-12
Conversation with PROSIM Program
216
8-13
Conversation with PRODEP Program
225
8-14
Functional Features of the Various Programs
242
- 12 -
LIST OF FIGURES
Title
Figure No.
Page
2-1
C ertainty-Equivalence Curves
45
4-1
Risk-Return Scatter Diagram
102
7-1
Graph of the Function c(Z+ )
155
7-2
Earnings-Per-Share
7-3
Ownership Dilution Function
163
7 -4
Debt -to -Equity Function
168
7-5
Piecewise Linearization of the Solvency Penalty
Dilution Function
159
Function
169
8-1
Cumulative Probability Distribution Function
213
D-1
Linear Risk-Return Assumption
289
D-2
Rejectability Area Under No Capital Rationing
290
D-3
Rejectability Area Under Capital Rationing
291
- 13 -
LIST OF FLOWCHARTS
Flowchart
Title
No.
Page
1
A Framework
2
Market Valuation - Adjusted P/E Method
125
3
Market Valuation - Discounted Cash Flow
126
4
Value to the Buyer
127
5
Market Valuation - ROI Approach
128
of Analysis
124
- 14-
CHAPTER I
Introduction
When two companies combine assets in exchange for securities
and only one company survives (although the other still exists as an
operating entity), the transaction is called a merger.
pany is formed, there has been a consolidation.
If a new com-
When one company
is purchased by another and completely absorbed, so that the selling
company no longer exists, an acquisition has taken place. In practice,
these definitions tend to become blurred, and the terms are usually
used interchangeably.
Why do companies merge? A general answer cannot be provided. Companies take the merger and acquisitions route for several
reasons.
Growth is probably the most common reason.
Expansion
through acquisition of other companies may be quicker than internal
growth, may prove less costly in the long run, and may decrease potential competition as well. A company may improve its financial
position by acquiring firms with unutilized borrowing capacity, or with
losses which can be recovered through tax carry-overs.
Others seek
the achievement of operating economies through the consolidation of
certain departments (accounting, marketing, clerical) and of production facilities. Closely related to operating economies is the
-15acquisition of management, as a route to obtain an aggressive team
which may foster the long run wealth of the stockholders. A merger
may improve a company's marketing position by reducing its reliance
on a particular type of customer, and stabilize the cyclical nature of
its business.
Different as they may appear, all of these motives strive towards the attainment of a common objective: the creation of an entity
whose market value is greater than the sum of the values of the merging firms considered as separate entities.
This phenomenon, known
as synergy, is central to the economic justification of mergers and
acquisitions.
Among the problems facing a corporation in evaluating a merger candidate is that of determining the price to be offered.
This price
may be viewed as the sum of the candidate's fair market value plus a
premium justified by
the extra benefits generated by the merger
and accruing to the stockholders of the corporation.
Different com-
panies may assess differently the value of these benefits.
This ex-
plains why a range of prices rather than a single value may be placed
on the same assets.
Therefore,
it will be suggested in the course of this thesis,
that the process of premerger valuation be structured in such a way
as to allow explicit and separate valuation of the fair market value of
-16-
the firm to be acquired, and of the synergistic benefits expected to
accrue as a result of the merger.
There are, of course, a number of nonfinancial factors which
must be taken into account, such as personnel, image, entry in new mar-
kets, and technological considerations. Because some of these factors
may defy quantification, our analysis will be limited to those which
are of a financial nature.
The purpose of this thesis is (i) to illustrate some of the methods and techniques that are available and have been used in the evaluation of firms for acquisition purposes, (ii) to present, drawing upon
this background, a framework of analysis and provide practical guidelines to establish a maximum price to be offered for an acquisition,
(iii) to examine the financial impact of some of the issues involved in
price negotiations, such as media of exchange, type of transaction,
schedule and forms of payment, and related tax implications, (iv) to
investigate the general use of computers in support of merger activities, (v) to illustrate an interactive program developed to assist the
manager in structuring a financial package consistent with several
operational and financial goals.
The scenario that we have chosen is that of a publicly traded
holding company buying a privately-held corporation.
We, therefore,
develop our analysis under the assumption that there does not exist
-17-
a market price for the shares of the firm to be acquired.
We further
assume that the acquired business after the acquisition will be run
as an independent entity. This will allow us to restrict the analysis
of synergism to those benefits which are financial in nature, although
the proposed framework will be general enough to take operational
benefits into consideration as well.
We would have liked to avail ourselves of more data about
valuation techniques than we were able to collect and examine.
The
difficulty of uncovering such information, as employed by companies
involved in the process of merger and acquisitions, or in consulting,
was underestimated. Firms, are, as we have found, rather secretive
about the methods that they employ in valuation analysis.
Following is an outline of this thesis.
In Chapter II, we examine three methods of evaluating the fair
market value of a firm:
asset valuation, market valuation and
the valuation of potential cash flows. In Appendix A, we present an
example of an implementation of the market valuation analysis through
the adjusted P/E method. Rather than determining a single price, the
value of the firm will be bounded within a range of values.
In Chap-
ter III, we introduce a framework for evaluating the acquisition from
the buyer's point of view. This will lead us to the explicit evaluation
of the net benefits available from the merger and to a technique for
-18-
comparing and selecting investments which are in a different risk class
from that of the acquiring firm.
Appendices C and D deal with the
practical issue of determining the appropriate discount rates and des cribe the concept of risk-equivalent rate of return.
In Chapter IV, we consider some of the other factors that usually
enter the acquisition analysis and which may ultimately have an impact
on the determination of value. We specifically expound on the use of
earnings per share dilution and ROI as valuation criteria in premerger
analysis.
Furthermore,
in looking at the acquisition as part of the in-
vestment portfolio of the acquirer, we consider the issue of diversification and the benefits which may be thereby derived.
In Chapter V we recognize that the psychological and economic
expectations of the seller have a large impact on negotiations.
In prac-
tice, the expectations of the seller can be met by structuring the deal
in a way consistent with those expectations.
type of transaction,
Tax considerations, the
the financial package to be offered are briefly con-
sidered as means available to the buyer to affect negotiations.
In particular,
the use of contingent contracts is seen as a help-
ful approach to bridge the gap that may separate the buyer and the
seller with respect to their individual assessment of fair terms of
exchange.
-19-
In Chapter VI, we suggest a procedural framework to be used
to work through the analysis of a prospective acquisition candidate. This
model represents a synthesis of the techniques and methods described
in the course of this thesis.
Chapter VII follows with an application of goal programming to
the problem of structuring a financial package. The technique allows the
decision-maker to explore several combinations of financial packages
and choose the one that comes closest to satisfying his several internal
goals as well as meeting the seller's requests.
Chapter VIII presents the results of our survey of computer
programs which have been developed over the last years and which
support in some way or another the process of financial merger analysis.
In Chapter IX, we present a preliminary
version of our own
interactive computer program, designed to aid the decision-maker
structure a merger package in accordance with several specified goals.
Finally, in Chapter X we present a brief conclusion on our work
and provide suggestions for further research and developments.
-20 CHAPTER II
Fair Market Value: Valuation Methods
Since 1954, federal tax regulations have specified the use of
fair market value in corporate tax returns.
This term has become
the basis of value used in valuing corporations.
Fair market value is generally defined as:
· . . the price at which property would change hands between
a willing buyer and a willing seller, each having reasonable
knowledge of all pertiPent facts and neither being under compulsion to buy or sell .
According to this definition, the fair market value (FMV) of
a corporation relates to the value of its ownership, and therefore,
corresponds to the market value of its equity. Stated in other terms,
FMV is a measure of a firm's total market value less the market value
of any outstanding debt. In mathematical terms, this may be summarized as:
FMV = E = V-D
Therefore, in order to determine FMV, it is possible to either
(i) determine E directly or (ii) determine V and substract D.Although
1John
Heath, Jr., "Valuation Factors and Techniques in
Mergers and Acquisitions", Financial Executive, April 1972, pp. 34-43.
-21both approaches are quite similar from a computational viewpoint,
they are conceptually different.
In the first case, the firm is valued
from the equity holders standpoint, and, therefore, only the benefits
accruing to the firm's shareholders are taken into consideration. In
the second case, the company is first viewed globally, and correspondingly, all of its cash flow (flows to the shareholders plus interest payments to the debt holders) enter the determination of V; E is then
determined by substracting from V the market value D of the debt out -
standing. If the valued firm is unlevered (all equity) both approaches
are identical. It is worth noticing that the capital structure of the
firm is taken into account by both approaches.
In the course of this chapter, we shall examine the three valuation methods which are most commonly used to determine the FMV of
a firm:
i.
The Net Asset' Valuation Method proceeds to establish
the value of the whole enterprise and of each of its principal
elements, in proper relationship to each other and to the whole.
This value, net of any long-term debt, determines the firm's
fair market value.
ii.
The Market Valuation Method assigns a FMV to a com-
pany by submitting it to a comparison with similar public
companies in the same industry grouping.
-22 iii.
The Valuation of Potential Cash Flows Method deter-
mines a firm's value by discounting into the present the firm's
estimated future stream of cash flows.
To the extent that each valuation approach may yield a different value, these may be viewed as providing a reasonable range for
the firm's fair market value. The lowerbound of this range can be
considered to be the net liquidating value of the company's assets.
In what follows, we examine each of these valuation approaches.
-23 A.
Net Asset Valuation Approach
The importance of asset valuation can be illustrated through a
simple consideration.
Assume that two companies are exactly alike,
both in terms of their operating statements and their balance sheets.
Do the two companies necessarily have the same fair market value?
Clearly not.
An in depth analysis of the value and type of assets to be acquired can provide a much clearer picture of the worth of the business.
"The economic worth of any given asset is not the amount of its original
cost less accumulated depreciation, but rather an estimate of how much
better off the business is at a certain date for having it.
Therefore,
value must be ascertained by studying income stream and potential ob-
solence factors, niarket forces and current replacement costs." 2
Hence, rather than accepting book value as representing the
true economic value of the assets of the seller,
one should have the
assets appraised in order to establish their fair market value.
The Accounting Principle Board, in Opinion 16, suggests gen-
eral guidelines for assessing the fair market value of assets and liabilities. Establishing these values usually requires that adjustements be
made to the book values at which these assets appear on the seller's
balance sheet.
2
John M. Parker, "The Key Role of Property Appraisals in
Mergers and Acquisitions," Financial Executive, September 1972,p. 20
-24 These adjustements having being made, one can compute the
asset value of the enterprise using the simple formula suggested by
Heath: 3
E = WC + PP
+ I
in which WC represents working capital, PP represents plant and property and I represents intangibles.
In the same article, Heath also
provides a useful checklist of the principal classes of assets in each
category.
The above formula gives a going concern value of the firm.
Alternatively, one can also compute the liquidation value. This value
is arrived at by taking the fair market value of the assets and liabilities and applying appropriate adjustements to more closely reflect the
realizable value that might be obtained under a forced sale situation.
Liquidation value is important as it provides the appraiser with a lower
bound to the range of possible prices that he might want to consider.
There are additional reasons which suggest careful evaluation of
the assets of the seller:
1.
The value of the assets provides an indication of the
borrowing capacity that will be available if the assets are used
as collateral for bank loans.
2.
Knowledge of the remaining useful life of the assets allows
forecasting future capital outlays required in support of operations.
3 Heath,
op. cit.
-253.
For tax avoidance purposes, the owners of closely held
corporations tend to accumulate earnings within the corporate
shell.
These appear in assets which are not essential to the
operations of the business. These assets can, therefore, be
liquidated, thus effectively reducing the purchase price of the
acquisition.
4.
In many cases, appraisals can motivate the basis for a
shift in the emphasis for negotiations: the possibility of buying
the assets, rather than the entire business, might be brought
into the open.
Moreover, one must consider the accounting method that will be
applied to record the transaction on the books of the combined entity,
as this will ultimately determine the kind of liabilities or tax shelters
that one may obtain from carrying those assets.
The Net Asset Value of the firm is finally determined by subtracting from the computed Asset Value the market value of any long-
term liabilities.
-26 B.
Market Valuation Approach
When the company to be acquired is a publicly held company and
its stock is traded over an active exchange, there exists a strong inclination to value such company on the basis of the market price of its
shares.
In other words, even though one might have reason to believe
that current market price is not representative of the intrinsic value of
the firm, it may be politically and psychologically quite difficult for
either buyer or seller to be convinced that the company is worth any-
thing more or less than the market value of its shares.
In the case of a closely held company, the stock is not traded in
the open market.
However, because in the long-run the market place
tends to provide a much more reliable indication of the intrinsic value
of the firm, one can make use of publicly available information on companies in the same industry and of similar size and risk class to evaluate
by comparison the fair market price of privately held corporations.
The process of selecting comparable corporations and computing significant indicators to be applied as a valuation guide, is needless
to say, a complex problem and a highly judgemental exercise. Besides
selecting companies that have comparable trends in growth and income
and a comparable capitalization structure,
one has to make sure that
the accounting practices of the companies used in this comparison do not
distort the earnings or assets picture. If any differences can be dis closed, adjustments should be made to eliminate undesired impacts.
-27-
The object of this search is to find a class of similar firms by
looking at various ratios which are selected as being of primary importance in the valuation of the particular situation.
The first knotty issue has to do with the selection of standard
ratios appropriate to the company's state of development, seasonal
patterns, etc. Important sources of average ratios for a given industry can be found in Dunn and Bradstreet's,
Moody's and Standard and
Poor's Manuals. Alternatively, trade associations records may come
handy. Finally, ratios can be computed directly from data in annual
reports of companies in the same industry.
Several limitations in the
use of these ratios have been enumerated:
1.
Only numerical items are being evaluated.
2.
Management can influence those ratios.
3.
Different accounting practices in depreciation, income
recognition intangible assets, etc. may be misleading.
4.
Different definitions of common ratios is given by differ-
ent analysts.
But given that standards have been selected and computed, the
second issue becomes, what relative weighing do you give to each ratio?
Some ratios will relate to the profitability of the business, others to
its liquidity, others to its financial structure and to the risk profile;
-28-
still others to the assets available, or to the capability of paying out
dividends. The relative weighing becomes a matter of preference and
can best be treated by making individual assessment and measuring
their direct consequences in terms of the outcomes.
Adjustements
can be made to reflect lack of comparability, lack of marketability and
almost anything the appraiser cares to quantify in order to deal with
the uncertainties involved.
This approach is extensively used by investment bankers in
pricing of new issues: the value of a company is established mainly in
relation to other companies in the market place.
It should be noted
how, given the difference in objectives between going public and selling
out, the value given to the stock may ultimately be different.
In the
going-public case, one is essentially concerned with establishing the
value at which average blocks of minority shares will be traded.
In
the case of an acquisition, a premium over and above the market value
of the shares is usually paid to reflect the added value of control.
In Appendix A, we provide a description and an example illus trating how the market valuation technique is actually implemented by
valuation practicioners.
As may be observed, the Market Valuation Technique establishes the Fair Market Value of a firm by directly assessing the value
of its equity.
-29C.
Valuation of Potential Cash Flows
The fundamental characteristics of business assets is that they
give rise to income flows. Sometimes this flow is easy to determine
and measure; at other times, the cash flows attributable to the assets
must be estimated.
However, regardless of the difficulties of measur-
ing income flows, it is the prospective revenues fromassets that give
them value.
In determining the fair market value of a firm, it is, therefore,
essential to estimate and value the cash throw-offs expected to occur
over future years. The process becomes increasingly difficult as the
degree of certainty with which the receipts can be forecasted decreases.
Several valuation techniques have been developed to value an
asset on the basis of the expected stream of its future cash flows. From
a conceptual viewpoint, all of them require that
i.
Future cash flows be estimated.
ii.
The uncertainty inherent to these flows be ascertained.
iii.
The value given to the stream of estimated cash flows
be adjusted to reflect the uncertainties involved.
Whilst the conceptual framework used is the same, what differ-
entiates the various techniques is the way in which uncertainty is
treated.
In what follows, we shall describe the three main techniques
which are presently used to value the potential cash flows of an asset.
-30-
1.
i.
Discounted Cash-Flow (DCF) Technique
ii.
Certainty Equivalent Technique
iii.
Probability Distribution Technique
Discounted Cash Flow (DCF) Technique
This procedure, alternatively denoted as the capitalization-of-
cash flows method of valuation, involves (i) estimating the future net
cash flows4 attributable to the firm, (ii) determining a terminal
value to represent all cash flows expected to accrue beyond a selected
horizon date n, (iii) selecting the capitalization or discount rate r that
most appropriately takes the uncertainty of the cash flows into account,
and (iv) determining the present value of the stream of cash flows (us -
ing the selected rate as the discount rate). Mathematically, this is
expressed as:
n
CASH FLOWt
t=1
1. 1
Cash-Flow
(1 + r)
+ TER VALUE
(1 +r) n
Projections
In order to estimate future cash flows, an analyst must generate pro-forma cash flow statements for all years up to a defined
horizon year, and determine a terminal value to be used as a proxy
for all those cash flows expected to accrue beyond the chosen horizon
4By "net cash flows" we intend: expected earnings after taxes
and interest + depreciation - required investments.
-31year.
To do this, the analyst must forecast future income, working
capital, capital expenditures, depreciation and all other items affecting cash flow. The greatest problem lies with the assessment of
earnings over time. In order to forecast future earnings, he must
first become familiar with historical performance data as available
through past operating statements of the company. From this analysis, he tries to determine why the past record was what it was. As
the conditions that created the past trend become understood, the
analyst must then question whether these conditions are likely to persist
in the future.
If they are, projections can be made based on this assump-
tion; otherwise, the impact of foreseeable changes must be estimated
and incorporated in the forecasts.
The process is invaluable in forcing
the analyst to take into consideration the many variables that can influence the particular business.
Since the entire approach is based on
valuing future events, which are uncertain at best, one should look at
a range of possible values rather than at a single value.
The greater
the uncertainty, the larger will be the spread between the most optimis -
tic and pessimistic forecast.
Various mathematical models are available to represent future
growth in earnings under all kinds of different assumptions (such as
constant stream, growth at historic average rate, constant growth in
each year or time-varying rates of growth).
-32 Statistical techniques can be of help in analyzing past data.
Industry projected data can be usefully tapped in looking at future
growth potential, but when a company operates in more than one
industry, this may pose serious identification problems. Several
methods of performing analysis of growth can be found in classical
books of investment analysis.
and it is beyond the scope of our work
to cover this analysis. In practice, the process of projecting earnings
requires a contribution from marketing, production and finance people.
The marketing people will forecast sales, prices, selling expenditures;
the production people will estimate plant requirement and manufacturing
costs on the basis of projected sales; the finance experts will incorporate these estimates and translate them into projected earnings and finally,
pro-forma cash-flow statements can be generated.
1.2
Terminal Value
The analyst must make a decision regarding the time horizon
over which the cash flows are simulated, and forecast the terminal
value that can be attributed to the company at the end of the time
horizon period. The time horizon should be set as far out into the
future as the analyst feels he can make reasonable predictions.
minimum useful projection period seems to be five years.
A
Many man-
agers would argue that the level of uncertainty is such that they feel
5 J.
B. Cohen, E. D. Zinbarg.
folio Management, Irwin 1967.
Investment Analysis and Port-
-33-
incapable or unwilling to make projections much beyond a year or two.
But the same managers might feel quite comfortable in recommending
a buy decision on such basis, thereby committing long-term resources
to a project whose return is undefined beyond the first year or two.
The terminal value is used as proxy for the cash flow generated
by the business far into the future, when it becomes too difficult to
model relationships or assess probabilities.
Terminal value can take on a critical role in establishing a market value for a given venture.
It is particularly important in high-
potential ventures, where the investor is looking for large capital gains
in selling out the company, after having operated it for a few years. Because during this time the net cash flows may be negative in every year,
the return can only come from a higher P/E multiple attached to the
terminal value.
In the context of an acquisition, the assumptions made
about this value can have a large impact on the decision of whether or
not to go ahead with the acquisition.
Several models can be used for assigning a terminal value. One
can have the terminal value be a specified market value at the end of
the horizon. Alternatively, one can assume simple cash flow patterns,
such as constant cash flow in each year following the horizon date, or
a compound growth rate or any combination of the two. In Table 16, we
have reproduced six models of assigning a terminal value.
6 Prof.
J. S. Hammond III, Teaching Note 4-172-273, Harvard
Business School, 1972.
-34-
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-37 -
1. 3
Discount
Rate
The rate used to discount into the present the projected stream
of cash flows can be viewed as consisting of two elements.
The first
corresponds to a measure of the time value of money, and is usually
taken to be the risk-free rate, i. The second component corresponds
to the premium, over and above the risk-free rate, usually required to
induce the investor to take on risk.
The risk premium can be further
broken down into two components: a premnium for business or operat , and a premium for financial risk
ing risk
4. The first is caused by
the inherent risk of doing business in a given industry, i. e., by the
relative dispersion of the probability distribution of possible future
operating income. The second, the premium for financial risk, reflects
the volatility in earnings available to the stockholders of a firm, as well
as the probability of insolvency, which is a function of the firm's degree
of leverage.
The discount rate can thus be viewed as being the sum of three
factors
7
r =i+] +
7
Van Horne, op. cit.,
pp.
-38-
This rate represents the minimum rate of return required by
investors for investing in the firm.
In Appendix B, we have provided
a list of factors which may affect both the operational and the financial
risk premiums.
The main source from which an estimate of the appropriate discount rate can be obtained is the securities market for stocks of companies operating in the same industry.
Of the several techniques avail-
able for estimating r from the market, we will comment on the DCF
approach, mathematical probabilistic models and simulations.
The basic rationale for looking at the stocks of companies
operating in the same industry grouping as the firm being valuated is
that at any point in time, securities are so priced that all securities
within the same risk class offer the same expected rate of return.
Moreover, stock prices reflect the present value, discounted at r
of the stream of expected dividends Dt , i. e.,
00
Po
=
(2. 1)
t=l 1
The idea, therefore, is to estimate what investors expect in
the way of future dividends, and infer r* from the observed price PO
r is the rate of return that investors demand, on the average, for
investing in that industry.
Although the concept is clear enough,
-39-
important problems emerge in estimating the size and time pattern
of the stream of benefits.
Moreover,if the evaluated firm cannot be
viewed as a typical firm within its industry, r will not represent an
unbiased estimate of the rate of return on investment r that investors
may require to invest in that firm.
This will lead us to a second-level problem, namely: what
*
adjustements to r should we make to match the perceived differences
of operating or financial risk that the firm may present relative to the
average firm in its industry?
In what follows, we will first discuss
possible ways of estimating r and we will then proceed to consider
how r
can be adjusted to obtain r.
In order to aid in the resolution of these problems, Equation
(2. 1) can be written as8:
EPS 1
c
Po
Dt - EPS 1
t
(2. 2)
t=l
where the second term on the right-hand side can be interpreted as
the net present value of future growth opportunities.
With Equation
(2. 1) so expressed, a number of simplifications are usually made in
order to obtain estimates of r . Firstly, if the dividend stream is
8 Stewart
C. Myers, "The Application of Finance Theory to
Public Utility Rate Cases", The Bell Journal of Economics and
Management Science, Vol. 3, No. 1, Spring 1972.
-40 assumed to continue to grow indefinitely at some rate g, which is less
than r , Equation (2. 2) simplifies to:
D
Po
=
*
r -g
*
from which r is obtained as:
r
*
-
D1
P
+g
(2. 3)
Secondly, if it is assumed (i) that earnings per share (EPS) in any one
year are representative of "normal" long-run earnings of the firm,
(ii) that all earnings are paid out as dividends, and (iii) that the firm's
net present value of future investments is zero (all investments yield
exactly r on the average), Equation (2. 2) resolves to:
EPS
r
1
=
o
1
PO/EPS
Because of the simplicity of this formula, and ease of obtaining values for Po and EPS,the value for r thus determined has found
widespread use as the appropriate rate of return required by investors.
We wish to point out, however, that because of the assumptions made,
this value generally underestimates the actual rate of return which
investors may require for investing in a particular industry. To this
-41extent, the inverse of the P/E ratio of an industry should be used with
caution and awareness of its implications when trying to estimate the
appropriate discount rate for an industry.
The problem of adjusting r to match any peculiarites of the
firm being evaluatedwith respect to its industry, does not have a general solution.
In practice, r is determined by adjusting upward or
downward the industry's rate of return r to denote any amount of
operating risk and/or financial risk, above or below the firm's indus try averages.
These adjustements for risk yield what is usually re-
ferred to as the risk-adjusted discount rate.
The techniques which aid in adjusting r to the firm's proper
risk level, focus on those factors which may affect the rate of return
required by investors (see Appendix B), and make adjustements on
*
r by comparing the firm's specific attributes to those of its industry's
(see Appendix A).
When probabilistic and simulation models are used to obtain
estimates of r, the future volatility of cash flows or of the operating
variables which affect cash flows is captured in mathematical terms
9
and compared with the inherent uncertainty of returns of the equity
shares of companies operating in the same industry.
This comparative
analysis, in turn, leads to the estimation of an appropriate discount
rate.
-
-
9 We
dwell with these models in the following section.
-42 In conclusion, the risk-adjusted discount rate, as may be esti-
mated from a comparison with other firms in the same industry, has
a great deal of intuitive appeal; it makes sense to shoot for a higher
rate of return when a firm's risk characteristics are above the indus try average, and to do the opposite when the firm's future returns are
less risky.
According to this rule of thumb, the higher the risk, the higher
the discount rate, and the lower the fair market value to be attributed
to the firm.
Because this concept is simple and provides for the in-
corporation of individual risk preferences, its use has already gained
wide acceptance as a valuation and capital budgeting technique.
The
main shortcoming of the approach, however, stems from the difficulty
of determining the discount or capitalization rate which correctly com-
pensates for a firm's risk deviations from its industry's average. This
has lead many firm's and analysts to use a single and unnecessarily
high discount rate for their investment and capital budgeting needs.
Other disadvantages of the risk-adjusted discount rate approach
are:
i.
Because the selection of the risk-adjusted discount rate
is somewhat subjective, it is possible that the analyst may not
make consistent choices.
-43 Robichek and Myers 1 0 have illustrated how the use of a
ii.
constant discount rate for every year actually implies an increasing time pattern for risk. Because in the vast majority
of business situations, the further the returns,the more likely
they are to increase in uncertainty, the use of a constant risk-
adjusted rate may actually be appropriate. Nevertheless, the
amount of this increase is not directly specifiable by the analyst.
1.4
Present Value of Cash Flows
The fair market value of the firm is finally determined by dis -
counting, at the risk-adjusted rate r, the estimated stream of cash flows
and the terminal value.
=
n,
Mathematically, this is expressed as:
C CASH
FLOW
CASHFLOWt
(1 + r) t
+ TER VALUE
(1 + r) n
We remind the reader that CASH FLOWt represents expected
earnings after taxes and interest plus depreciation less required investments in period t.
Prentice
A. A. Robichek and S. C. Myers, Optimal Financing Decisions,
Hall, 1965, pp. 83.
-44-
2.
Certainty Equivalent Technique
Given the limitations of the discount rate technique, the cer-
tainty equivalent approach has been offered as a more realistic and
theoretically more powerful alternative to deal with risk
. The pro-
cedure consists in adjusting the numerators of the DCF formula to
yield for each period what the manager perceives as a certainty
equivalent cash flow. That is, all estimated cash flows are multiplied
by a coefficient that converts the uncertain cash flow to one equivalent
sum of money which the manager would be indifferent to receive with
certainty, in lieu of the uncertain cash flows. The certainty equiva-
lents are then discounted to the present value using the riskless rate
as the discount rate to avoid double counting risk.
This approach may be expressed as:
oo
a
CASHFLOW.
t
PV =
. J=*1
t3(1 +i)j
(2. 4)
where at, the certainty equivalent coefficient for period t, varies between 0 and 1, inversely with the degree of risk.
More precisely, at
is the coefficient that, in each period, makes the manager indifferent
between: the certain cash flow At and its risky counterpart At, i. e.:
at -
At
At
Idem.,
p. 80
-45 The certainty equivalent coefficient can be specified to be different in
each period, thereby easily compensating for time-varying degrees of
perceived risk.
The maximum fair market value to be attributed to a firm is
equal to its present value, as computed in Equation (2.4)
The use of this technique is predicated on the manager's ability
to represent the market's "trade-off" between certain cash flows and
progressively riskier ones. The locus of such "trade-offs" defines
what is generally denoted as a set of certainty equivalence curves,
which are graphed in Figure
2. 1.
Risk
a
Return
A
At
A3
-
Figure 2-1
*
-46 According to this graph, we can arrive at the certainty equivalent of
any point lying above the X-axis (o
0), by seeing where the certainty
equivalent curve that passes through the point intersects the X-axis
(a = 0).
The disadvantage of the technique resides in the fact that in
most cases, it is difficult to give at sufficient empirical meaning to
make them useful in practice.
Moreover, the technique is rather
cumbersome insofar as it requires the user to select an at for each
period; if cash flows vary over a large range, the number of certainty
equivalency curves to be constructed, assuming that they can be specified, would in any case be very large.
On the other hand, the method
makes it possible to value firms and rank them according to their ex-
pected profitability.
-47 -
3.
Probability Distribution Analysis
Both the risk-adjusted discount rate and the certainty equiva-
lent coefficients to be used in discounting the future cash flows of an
investment are determined by taking the variability, thus the risk, of
these cash flows into consideration. Thereafter, a single value for
each past period is selected and the present value of the project is calculated deterministically as a single point estimate.
A more powerful
model for dealing with the uncertainty of a project, considers the probability distribution of each flow and computes the resulting probability
distribution of net present values, to yield a complete profile of the
possible final outcomes. In describing an investment through a probability curve of its future outcomes, the decision-maker has available
an explicit graphical representation of the variability of the returns
from the project. Using this information, the riskiness of the investment can be evaluated much more realistically than by focusing on a
single number.
The probability distribution of any variable can be characterized
using two parameters,
viation.
its expected arithmetic mean and standard de-
Unless one makes specific assumptions, the shape of the
distribution is not univocally determined:
a skewness parameter should
also be specified in order to exhaustively characterize the distribution
curve.
With normal distributions, the mean Land standard deviation a
completely describe the distribution, which has the characteristic
shape.
bell
-48-
The expected value of the present value of a series of independent
cash flows A o , A
. . .'An, each having an expected value
E(At) is:
E(At)
Et)
E(PV) =
t=l (1 + i)
t-1~~1/
n
o(PV)
1/2
=
t=1
The appropriate discount rate to be used is the riskless rate.
To make use of a higher rate would actually result in double counting
the risk of the expected returns.
the dispersion of E(PV) can also be calculated
Furthermore,
as the present value of each period's a t , discounted at the riskless rate.
This, however, may be interpreted as implying the existence of a time
preference for risk.
Although we cannot provide an answer to this
question, it would seem that if risk is to be discounted at all, the usage
of a higher discount rate would underestimate the present value of the
There are a few investments for whichthe net cash flows are
completely independent of each other. If we assume each cash flow At
to consist of a component At which varies independently and a component At which is directly proportional to the A" of its preceding period,
the standard deviation of the PV of At's is given by:
n
2(Ath o Vn
AtA") 2
a
t
t
a=
(1+ i) 2t
( 1 + k)
For an expansion on this point, see J. T. Mao, Quantitative Analysis
of Financial Decisions. The MacMillan Company, 1969, p. 276.
-49-
expected cash flows' standard error of return3.
When dealing with normal distribution
functions, each E(At)
is equal to the arithmetic mean t of its pertinent distribution. Furthermore, to the extent that the sum of n normally distributed random
variables is itself a normally distributed random variable, each At is
normally distributed, E(PV) will also be normally distributed. Through-
out this thesis, for purposes of simplicity, we shall assume normality
and independence for the cash flows generated by a firm.
Once the E(PV) and o(PV) have been computed for the future
cash flows of a firm, it is possible to compute its fair market value
through the certainty-equivalent
approach.
Alternatively, a simpler approach which avoids the problem
of specifying a series of certainty equivalent curves, consists in using
the market's risk-return trade-off curve to determine (i) the probability index Pm required on investments of riskiness
(PV), and (ii) the
fair market value V3 such that
E(PV) - V3
V3
= P
Solving for V3 yields:
V3 = E(PV)
1 +p
13 Weston and Brigham use the risk-adjusted discount rate for
this purpose. See Weston and Brigham, op. cit., p. 249
-50-
The shortcoming of the probability assignment approach is that
it requires the market risk-return indifference curve to be specified.
However, in contrast with the certainty equivalence approach, only one
curve has to be defined.
This curve can be constructed by plotting on
a scatter diagram a series of risk-rate
of return combinations as found
in the securities market and by fitting through the points a least square
second degree polynominal.
Conceptually, the major advantage of this method is that it provides the analyst with a complete spectrum of possible present values,
rather than with a single number.
When the conditions of independence and normality do not hold,
it is useful to use probability trees and simulation models to derive
14
probabilistic estimates of future cash flows. Hillier , Hertz 15 and
Magee
have extensively dealt with these situations.
Because these approaches generally involve extensive computations, their practical use has been limited. With the increasing use of
computers as an aid to management decision-making, these techniques
are becoming more and more applicable.
14See Frederick S. Hillier, "The Derivation of Probabilistic
Information for the Evaluation of Risk Investments", Management
Science, IX (April 1963), pp. 443-57.
15DavidB. Hertz, "Risk Analysis in Capital Investments",
Harvard Business Review XLII (Jan.-Feb. 1964), pp. 95-106.
16 John
F. Magee, "How to Use Decision Trees in Capital
Investment", Harvard Business Review, XLII (Sept. -Oct. 1964),pp. 7995.
-51-
Hertz, for instance, makes use of Monte Carlo simulations
to derive probability distributions of future net cash flows from
management's estimates of individual operational variables (sales,
expenses, depreciation, etc.).
In conclusion, we suggest the fair market value of the firm be
determined as a range of prices arrived at by using the three basic
techniques illustrated in this chapter.
Each technique provides a dif-
ferent perspective. Correspondingly, the past, present and future
performance of the acquisition cnadidate are given due consideration
in an attempt to provide better insight than could otherwise be gained
by reporting to any one technique in isolation.
Several ways of estimating the uncertainty of future cash flows
have been presented.
Even though in the following chapters we will
not make explicit use of these techniques, we shall assume the
decision-maker will choose among them the most appropriate one to
assess risk as he perceives it.
-52CHAPTER III
Value to the Buyer: Valuation Methods
There is more to the valuation of a prospective acquisition than
merely computing its fair market value.
If that were the maximum
price worth paying for the acquisition, there would be no real point to
the merger.
In fact, it is because the acquisition's value as part of
the buyer's assets is generally greater than its fair market value, that
the prospect of merging the two entities is economically more advantageous than operating the two firms independently. This is the essence
of synergism.
The potential synergistic benefits to be gained from an acquisition may be quite diverse, including but not limited to: economies of
scale, increased market share, elimination of inefficiences in the acquired firm, diversification, better use of funds and new investment
opportunities, increased earning per shares, better management, tax
advantages, etc.
In order to capitalize on most of these benefits, it is usually
necessary to proceed towards a substantial integration of the operations
of the two firms. For other benefits, however, primarily financial in
nature, a minimal degree of integration is necessary.
To the extent that the main focus of this thesis is on the finan-
cial aspects emerging in acquisitions, we shall limit our discussion
-53-
on synergistic effects to those that are financial in nature.
In the first section of this chapter, we use the DCF technique,
as described in the previous chapter, to assess the impact of the ac-
quisition's estimated total cash flows upon the acquirer and thereby
derive the maximum price to be offered for it. The estimates of cash
flows embody the synergistic benefits involved in the merger.
In the second section, we present a framework of analysis
which leads to the determination of the maximum price to be offered
for the acquisition by focusing primarily on the cash flows expected
to be generated from the synergistic effects resulting from consolidation. The present value of these benefits is then added to the fair market value of the seller in order to determine the maximum price.
Throughout this chapter we shall make no explicit use of the
probabilistic techniques described in section C of Chapter II to deal
with the uncertainty of cash flows. In practice, however, in order to
consistently assess the risk inherent in various investments, the
decision-maker should make recourse to those techniques.
-54-
A.
Total Cash Flow Analysis
In the previous chapter, we presented the DCF technique as
one of the most pragmatic methods for computing the fair market value
of a firm.
The same technique
can be used by the acquirer to evaluate,
from his viewpoint, the stream of total cash available from the pro-
spective acquisition (i. e., the expected cash flows from the acquisition
on a "stand-alone" basis plus those which will derive from any syner-
gistic effects).
Because the acquirer will be able to modify the capital struc-
ture resulting from the merger, the valuation analysis should attempt
to measure the expected earning power of the total assets of the acqui-
sition, apart from considerations of financial structure.
In other words,
the acquisition shouldbe evaluated as an unlevered firm, and thereby
only in the light of its expected cash flows and operational risk. To this
extent, the definition given in Section C of Chapter II to "cash flows"
needs to be modified to reflect the fact that the prospective cash income from the acquisition must be estimated before interest charges.
The appropriate measure of cash flow to be used in any given
period is, therefore, the total amount that will be available to the acquirer, that is,total expected earnings after taxes (but before interest),
plus depreciation less any investment required in that period. We may
write this as:
-55 -
CASH FLOWt = EBIT t (1 - T c ) +Dept - It
The "discount rate" to be used in discounting the estimated
stream of cash flows must be the minimum rate of return that the
investment should earn to leave the value of the acquiring firm unchanged. Mathematically, this is expressed as:
dA
= dV
where
dA = purchase cost of assets acquired
dV = change in the acquirer's market value.
This point relates to the concept of cost of capital, which is the
cost paid by the firm for funds acquired from the capital markets. Different size and type of firms (i. e., public versus closely-held) have
different costs of capital, even if the operating risk of the projects they
invest in is the same.
In particular,
a public company will ceteris
paribus, generally have a lower cost of capital than a closely-held corporation, because of the higher liquidity it offers its investors and the
lower risk resulting from having to operate in conformance to SEC
regulations.
-56 -
To this extent, in determining the appropriate capitalization
rate to use in discounting the total cash flows which will become avail-
able to the buyer as a result of the merger, it is important to address
the issue of what impact the acquisition will have upon the risk inherent
to the acquirer's returns on equity prior to the merger.
Two cases are possible: either the acquisition's assets fall in
the same risk class as those of the acquirer, or they do not.
In the first case, the appropriate discount rate to be used is the
acquirer's
weighted average cost of capital, as defined in Appendix C:
D +r
cE+ D
P1 = (1 -T)il
E
E+D
where the subscript 1 indicates the purchasing firm.
In the second case, when the prospective acquisition falls in
a different risk class, one should use the risk-equivalent rate of return
p' as derived by Tuttle and Litzenberger and defined in Appendix C:
p
= (1 - T)
c
i
E' + D'
+
E' + D'
where D'/(E' + D')and E'/(E' + D') are the weights according to which
the acquisition must be financed if r1 is to remain unchanged.
This
-57 -
mode of financing poses no restrictions on the way the acquisition is
actually paid for, provided, however, that the required financial mix
is reached subsequently through appropriate amounts of borrowing or
lending. We expand on the risk-equivalent approach in Appendix D.
Having thus defined cash flows and the appropriate discount
rates to be used, the present value of the stream of total expected cash
flows from the acquisition can be computed to obtain its maximum value.
However, because this value has been obtained by assuming the
acquisition candidate to be unlevered, the maximum purchase price to
be offered is obtained by substracting from this value any outstanding
debt and obligations that the seller may have and that which the ac-
quirer will assume.
The shortcoming of using the total cash flow approach is that the
synergistic aspects of the merger are being considered as part of a
single stream of cash generated from the assets of the firm.
This poses two problems.
Firstly, the incremental benefits
deriving from the merger are not explicitly isolated. As a result, the
acquirer may fail to gain enough insight into what is actually being
gained by proceeding with the merger.
Secondly, because all cash
flows are lumped together and only one discount rate.is used, no explicit
recognition can be given to the fact that certain cash flows will have
different degrees of uncertainty.
1Depending on how the acquirer perceives the risk attached to
the synergistic cash flows, the discount rate can be adjusted upward
or downwardto reflect his attitude.
-58-
These deficiencies indicate that it would seem more appropriate
to isolate the synergistic and other cash flows, and use for each stream
a risk-differentiated discount rate.
In the following section, we will illustrate a framework of ana-
lysis which proceeds to determine the maximum price to be offered for
the acquisition in this manner.
-59 B.
Synergism: A Framework of Analysis 2
If we assume that Firm 1 is considering acquiring Firm 2 and
if we take RV1 to accurately reflect the fair market value 3 of Firm 1,
and RV2to represent the fair market value of Firm 2, then the real
value RV3 of the combined entity will be equal to:
RV3
= RV1 + RV2 + Present
value of synergistic
benefits
(3. 1)
In looking at the benefits and the costs pertaining to a possible
acquisition, we will use the following definitions:
Benefits: the difference between (1) the total present value of
the merged firm and (2) the sum of their values if they do not
merge.
Benefits
= ARV3 = RV3 - (RV1 + RV2)
(3. 2)
Costs: the difference between the amount paid for the acquired
firm and what it is worth as a separate entity. That is, the
"premium" paid for the acquisition.
1The
main ideas and the framework of analysis presented in
this section have been provided by Prof. S. C. Myers in "Evaluating
Mergers and Acquisitions", Sloan School of Management Teaching
Note, June 1971.
2 As
in Chapter II, the fair market of a firm is here defined to
represent the market value of its equity.
-60Cost = Premium
= PRICE - RV2
Usually, in evaluating a merger, firms are used to equate the
cash outlay to the total stream of cash flows available from the acquisition (including those of a synergistic nature).
This, in fact, was the
approach followed in Section A. Conversely, in the proposed framework, the manager is asked to evaluate separately the cash flows available from Firm 2 as if it continued to operate independently, and the
present value of the incremental benefits that are expected to be avail-
able, given that the two firms will be merged together. For this reason, it is convenient to define cost as only that part of the payment
which does not cover the fair market value of the firm.
Similarly,
benefits are defined as the dollar value that measures the degree to
which two firms are worth more together than apart.
The main ration-
ale behind this approach is to bring the synergistic aspects of the merger
into sharper focus and therebyprovide the acquirer with a better understanding of what premium over the fair market value he may offer for
the acquisition.
We will now proceed to elaborate on the relevant benefits and
costs, reminding the reader of the fact that Firm 1, in our specific
case, is a publicly-traded firm and Firm 2 is a closely-held corporation.
-611.
Benefits
The major benefits that may accrue to Firm 1 are:
1.
Excess debt capacity available in Firm 2.
2.
Liquidation of excess cash or unprofitable assets.
3.
Better access to funds: lower financing charges.
4.
Additional investment opportunities in new lines of
business.
5.
Divers ification
6.
Tax Benefits
7.
Operational Benefits
8.
Intangibles (image, entry in new markets, management,
etc. )
In the present value calculations, the cash flows from financial
benefits will generally have to be discounted at the acquirer's borrowing rate, whereas the cash flows derived from operations should be
discounted at the appropriate risk adjusted discount rate.
If we exclude
"Intangibles" which defy quantification, only "Operational Benefits" and
"Additional Investments" would be regarded as falling in the class of
operational benefits; all other benefits are financial. We will further
expand on the use of separate discount rates in Section 3.
-62 In what follows, we describe how to compute the dollar value
of the benefits and the costs.
i.
Excess Debt Capacity
The value of unused debt capacity is equal to the after-
tax interest payments on the additional portion of debt that can
be issued, discounted at the borrowing rate (i. e., the present
value of the potential tax shelter).
ii.
Excess Assets
If the liquidation value of any asset which is either not
essential or unprofitably used is over and above its net present
value to the firm, the asset can be liquidated and the value of
the firm be increased by the difference.
iii.
Lower Financing Charges
The benefit accruing to the combined entity is going to
be at least the difference between the borrowing rate for the
combined firm and the rate at which the seller could borrow at,
times whatever amount of financing is anticipated by the needs
of the acquired firm4
4 Several
studies have shown that within an industry the cost of
equity funds tends to decrease with the size of a firm. This effect,
however, has been found to be of minor importance. See Merton H.
Miller and Franco Modigliani, "Some Estimates of the Cost of Capital
to the Electric Utility Industry", American Economic Review, June
1966, pp. 339-340.
-63 -
iv.
Additional Investments
If the acquisition opens up new possibilities for subse-
quent capital investments, then the stream of cash after tax
less the stream of new investments, discounted at the riskadjusted discount rate should be considered as an additional
benefit accruing from the merger.
v.
Diversification
It is the differential benefit accruing to the firm for
taking on a project which lowers the overall risk of the firm.
The benefit is measured by the difference in price that would
be paid considering the project in the portfolio of the firm's
investments, as opposed to in isolation.
Given that Firm 2 is a closely-held corporation and
if Firm 1 stockholders would not otherwise be able to avail
themselves of the diversification benefits provided for by
Firm 2, diversification affects may be quite relevant to our
analysis.
subject.
In Chapter IV, we devote a whole section to this
-642.
Costs
In principle, the overall benefit from a merger is the present
value of the synergistic cash flow available for reinvestment.
The
present value of this benefit should be compared to the cost incurred
to obtain it.
Cost has been defined as the premium paid, i. e., the difference
between the payment for acquiring the firm and what the firm is worth
as a separate entity:
Cost = Value of assets paid to 2 by 1 - Real Value 2
= PRICE2 - RV2
The likely cost of a proposed acquisition varies depending on the type
of transaction to be adopted. For the cases where cash or stock are
used as transaction media, the costs are:
i.
Financing with Cash
In this case, the cost is simply the premium paid over
the acquisitions fair market value:
COST
= CASH - RV2
-65 ii.
Financing by Stock
The apparent cost is the premium paid over the fair
market value of the acquired firm:
Apparent Cost = NSI * P 1(0) - RV2
where NSI is the number of shares issued and P1(0) is the
market value of one share of Firm 1 at the time the deal is
considered.
However, this is not likely to be the real cost, because:
(i) the market price of the shares P1(0) could be over or understated; (ii) a portion of the benefits generated by the merger
will now accrue to shareholders of the acquired company.
Therefore, the true cost is:
True Cost = 1
where
NSI
NOS1 + NSI
and
RV3 - RV2
-66-
NOS 1 = number of shares outstanding in Firm 1
NSI
= number of shares issued
and : * RV3 indicates the real value of that portion of the merged
firms received by the shareholders of 2.
3.
Discount Rates
In this section, we attempt to be more specific about the discount rates to be used in the evaluation of the cash flows available to
the buyer as a result of the acquisition.
In so doing, we will make use
of formulas presented in Appendix C.
Let us rewrite Equation (3. 2) as:
RV3
- RV1 = RV2 + ARV3
(3.2a)
This relationship expresses the differential value between the combined entity (RV3) and the buying firm (RV1) as the sum of the intrinsic
value of the acquired firm (RV2) plus the incremental benefits (ARV3)
available from the merger.
The right-hand side of (3. 2a) thus repre-
sents the total present value of the acquisition. In order to compute
this value, we will, therefore,
evaluate RV2 and ARV3 independently
using different discount rates, as appropriate.
-67-
3. 1
Determination
of RV2
There are three different ways in which we can determine RV2.
a.
The first method corresponds to that used in Section A,
where we looked at the firm from the point of view of the inves tors in the market place and, therefore,
considered only the
cash flows available to the equity holders, i. e.,
CASH FLOW = EAIT + Depr - Invest
The appropriate discount rate to be used in this case is the
risk-adjusted market rate of return r 2.
b.
Alternatively, a second method considers the total
stream of cash flow expected to accrue from the firm's assets
independentlyof capital structure considerations, (hence after
taxes but before interest), i. e.,
CASH FLOWt = EBITt (1 - Tc) + Deprt - Investt
_=1_2
and discount it at the weighted average cost of capital of that
firm.
P2= (1- Tc)i
D2
E2
2
+ r2 E2 +
+
2
2
-68-
c.
Thirdly, RV2 may be determined by using the Adjusted
Present Value (APV) method (described in Appendix C). Accordingly, RV2 is determined as the sum of the value of the unlevered
firm (the firm assumed to be all-equity financed) and the present
value of the tax shelters provided by the firm's debt. The ap-
propriate discount ratio to be used in this case are
P02 for
the stream of operational cash flows, i. e.,
CASH FLOWt = EBITt(l - T c) + Deprt - Investt
and i for the tax shelters
TAX SHELTERt = i T c Dt
3. 2
Determination
of ARV3
In determining the present value of the synergistic cash flows,
it is necessary to distinguish between the several sources giving rise
to these incremental benefits, and use for each stream a discount rate
reflecting accurately its associated degree of risk. Accordingly, one
may use:
i.
ii, the borrowing rate of Firm 1, for the financial
benefits.
-69 -
ii.
Po2' the cost of equity of Firm 2 when considered un-
levered, for any operating benefits.
Recall that Po2 may be
derived from Firm's 2 cost of capital P2 by using the MN-M
relationship:
P o 2 (1 - T
P2
D/V)
or by using
(r -ipo2
(r
-
Po2)i
EBIT
(r EBIT
i)
= times interest earned
I
as derived in Appendix D.
4.
Price of the Acquisition
The maximum price to be paid for the acquisition, short of the
evaluation of intangibles, may finally be determined as:
PRICE2
= RV2 + PV benefits
(3. 3)
By looking at Equation (3. 2), we observe that if the negotiated price
equals RV2, Firm 1 has available the total value of the benefits at 0
cost. If the price equals RV2 + ARV3, then all synergistic benefits
accrue to the seller.
In between these bounds, the benefits from the
merger are shared between both seller and buyer.
-70Throughout this chapter, only tangible factors have been
brought into the analysis.
To the extent, however, that prior to the
final decision on the maximum price to be offered, intangibles usually
play a considerable role, we may expect the ultimate price to be adjusted in a subjective manner.
(continued on page 72)
PAGES (S) MISSING FROM ORIGINAL
-72 CHAPTER
IV
Other Factors in Determining the Acquistion Price
There are many variables and many conditions that management
may want to satisfy in establishing the price and the means of exchange
to be used in acquiring another business. These variables, when taken
globally into consideration, may contribute to the determination of value.
However, they do not per se indicate value.
Management is generally faced with a multiplicity of objectives
that it wishes to attain.
In practice, it will, therefore,
objective and aim at satisficing the others.
define a primary
These subgoals may range
from retaining a given percentage of ownership, to maintaining a certain
dividend payout ratio, from limiting short-term dilution in earnings per
share, to observing a given debt to equity ratio.
In fact, at any parti-
cular point in time, any one of these subgoals may become a goal in its
own right, as opposed to being merely regarded as a guidepost.
This has been the case with the controversial and widely debated
use of earnings per share dilution as a primary performance criteria in
merger activities. In the first section of the present chapter, we will
be looking at this issue in some detail.
In the second section, we will be commenting on the use of ROI
as one among other commonly used criteria for evaluating investments.
-73 Finally, we will consider the goal of diversification.
In so
doing, we will cease to look at the riskiness of an acquisition as an
isolated investment, rather we will view the firm to be acquired as
part of the portfolio of existing investments whose overall return is
to be made less volatile.
Earnings Per Share
A.
In the present section, our objective is to gain some perspective
intothis concept in order to suggest that EPS should not be re-
garded as a primary goal, but rather be used as one of several criteria,
useful in bounding the price of an acquisition.
Furthermore,
we will
provide and illustrate the use of a formula that can be used to determine the maximum price per share, which should be paid for a nonpublic firm, given that the buyer requires no EPS dilution by a specified
year.
1.
The Chain Letter Effect
There is a strong interest among those publicly held
companies which seek growth through acquisitions to have the
highest possible market price accrue to their stock. This is
because these companies usually make use of their common as
currency with which to buy other companies.
It follows that the
higher the price of the stock, the fewer the shares which need
to be issued to pay for a given acquisition and the lesser per-
-74-
centage of ownership that has to be given up to the new share-
holders. One should further consider that the smaller the total
number of shares outstanding after an acquisition, the higher
the earnings per share.
Obtaining an immediate increase in
earnings per share from an acquisition has two advantages.
First, with no change in the P/ E multiple, the price of the stock
goes up in proportion to the increase in earnings per share.
Secondly, since P/E ratios are favorably influenced by a rising
earnings trend, if the acquisition improves the earnings per
share picture, it is reasonable to expect an increase in the P/E
that the market attributes to the stock.
This would again propor-
tionally increase the price of the stock.
With a high P/E, a "growth" company can maintain its
image of growth by making successive financial acquisitions,
even though the acquired companies have themselves limited
growth prospects.
This is the so-called "chain letter" or "bootstrapping"
effect, which was at the basis of the conglomerate game back
in the twenties.
As long as companies with lower P/E ratios
than the P/ E of the purchaser are acquired, an immediate im provement in EPS for the combined entity results.
The company
may thereby enjoy an increase in the price of its stock, which would
further enhance new acquisition prospects.
Hence the interest
-75 -
in the short term impact of the acquisition on the price of their
stock of most companies involved in external growth.
Already in the twenties, this tactic proved to be a very
dangerous one, and many of the companies that tried to play
the same game in the sixties, found that it did not work any
better then. The reasons which account for the failure of this
short-sighted approach to acquiring firms are covered in what
follows.
2.
Short-Term Dilution
The rationale for avoiding short-term dilution stems
from the empirical observation that the market place seems
to overdiscount future earnings in the presence of short-term
dilution, at least in the immediate aftermath of the consolidation.
This constraint has traditionally posed severe limitations as to
the type of companies that can be acquired.
Companies with
excellent long-term prospects usually command a high P/E
multiple and even though future earnings, on a net present value
basis, may more than compensate for the short-term
effects, the deal is not considered.
diluting
In fact, it is precisely be-
cause too much emphasis has been put on short-term impact
that future earnings have suffered and many conglomerates
have therefore foundtheir long-run viability severely impaired.
-76In recent years, the "myth of dilution" has been at-
tacked by several financial experts 11
At stake is the fact that management has full respon-
sibility.of its shareholders and cannot disregard either the
short-term or the long-term impact of the investments that it
decides to make. Therefore,
avoiding short-term
dilution in
earnings should at least not prevent management from taking
on situations with good long-term potential.
Let us consider
the case of a company with a low P/E ratio and presumably
low growth, trying to acquire a company with higher growth
prospects and commanding a higher multiple. A large number
of shares would have to be swapped for a relatively small number of earnings, thus diluting the earnings of the acquiring company by more than the desired amount. In the face of a very
desirable situation, if long-term earnings for the combined
company show the desired growth rate, a financial package could
then be devised that minimizes the risk of present stockholders
in the short-run also.
If available, cash can be used to pay for the acquisition;
alternatively, the cash needed may be raised through a debt or
equity issue.
This medium of exchange would of course force
the acquired company to pay capital gains tax, which the seller
1J. F. Weston, The Determination of Share Exchange Ratios
in Mergers, The Corporate Merger, W. W. Alberts and J. E. Segall,
Univ. of Chicago Press,
1966
-77 might have to cover through a commensurate increase over
the purchase price that he would pay in a stock for stock swap.
Issuance of non-voting stock, such as common preferred,
will
also avoid dilution, but again the seller would have to pay capital gains tax on the transfer,
since only the exchange of voting
stock istreated as a tax-free exchange. Issuance of convertible
debentures or convertible preferred will in many cases allow a
tax-free exchange and avoid immediate dilution.
To achieve similar objectives, contingent payment contracts can be an ideal compromise.
With this technique, a
downpayment of stock is made at the time of closing the deal
and further payouts are made conditional upon future earnings
of the acquired company.
One final possibility is the installment sales agreement,
whereby the buyer agrees to pay no more than 30 percent of the
total agreed upon price in the initial year of the acquisition.
This has certain tax advantages for the seller, as capital gains
taxes may then be paid on contingent payments as they come due.
3.
Long-Term Dilution
We have so far discussed how short-term dilution of
EPS should be considered by management a guidepost rather
than an objective.
We have also noted how enough flexibility
-78exists in structuring the financial package to overcome most
of the undesired short-term dilution problems.
We must now turn to the use of this guidepost as an
indicator of long-term growth in the earnings of the overall
corporation.
Specifically, we have in mind the long-term
dilution effects that may result from the merger if the acquired
does not meet the same earnings goals planned for the consolidated entity. This concept is covered very effectively by
Fray-Ackerman , with the introduction of what they call the
"diversification gap".
On the assumption that a firm's acquisition program
is, as it should be, closely related to the attainment of clearly
identified corporate objectives, and on the assumption that
growth in EPS is a fundamental measure of economic performance, then "the EPS growth objectives provides the firm with
a way of planning acquisition activities for the long term". 3
The difference between the objective and the expected earnings
growth from current businesses (internal growth) over the
planning period constitutes a diversification gap. Each potential
acquisition can be evaluated in terms of its contribution to clos -
ing that gap with its future stream of earnings. A long-run
2L. L. Fray,
R. W. Ackerman,
Financial Evaluation of a
Potential Acquisition, Financial Executive, October 1967.
3Idem.
-79 dilution occurs if in the planning horizon year the earnings per
share issued (EPSI)for the acquired company are below the
earnings per share that the corporation has established as its
target for the planning horizon year.
Unless this happens, the
diversification gap will not decrease.
This long-term dilution
constraints set a ceiling on the price that can be paid for acquiring the business.
The article provides a clear example of how, if the
shares issued to acquire the business earn anything short of
the target EPS for the corporation as a whole, the diversification gap will widen.
Let us assume that purchaser P expects earnings from
his current business to grow at 8 percent per year for ten years
from the present level of $2/share; 5 million shares are currently outstanding and the price per share is $36 (P1). Its objective is to have a 10 percent growth in EPS over the next ten
The diversification
years.
gap (Div. Gap) is computed as
follows:
At target
growth rate
of
10%
EPS (10) = 2. 594 * $2 = $5. 19
8%
EPS (10) = 2. 159 * $2 = $4. 32
At the
expected
growth
rate
A = $0. 87
Div. Gap
= $. 87/share
* 5 M shares
= $4. 35M
-80-
So P in the tenth year will see its earnings per share $. 87 short
of target and a resulting gap of $4. 35M in profits.
Let us assume now that in an effort to reduce this gap,
P acquired company S's 800, 000 shares at $24 per share and it
does so by issuing:
$24 * 800,000/$36 = 533,333 shares
of its own common stock.
If S earnings are $800, 000, each share issued by P will
earn $800,000/533,333
= $1.50/share.
S is expected to have
a growth rate of 12 percent; the present earnings of $800, 000
will grow from $1. 50 to $4. 66 per share.
The earnings per share for the combined company will
recover from an initial dilution of $0. 05 and in the tenth year
will be $4. 36 rather than $4. 32 per share, as evidenced by the
following calculations
EPS
post merger
in Year 0
EPS
in 10th
year
5,000,000 * $200 + 533,333 *.
$1.955/sh
5, 533, 333
5,000,000 * $4. 32 + 533, 333 * $4.66 =$436/sh
5, 533, 333
-81-
In spite of this improvement in EPS fr the overall corporation,
the diversification gap has actually increased!
A = ($5. 19 - 4. 36) = $. 83/share
Div. Gap = $.83/sh
* 5, 533, 333 shares = $4,425, 000
representing an increase of $75,000 over the value that was pro-
jected for the corporation withoutthe acquisition.
In fact, unless S can be purchased at a price such that,
in Year 10, S will earn $5. 19 per each P share issued, dilution
with respect to the growth objective will occur.
The equation that allows the calculation of the maximum
P/E ratio that can be paid for company S can be derived as
follows:
EPSI (10)
-
E2(10)
ISH
E2(10) = E2(0) * (1 + g2)1 0
ISH = PRICE2
P1
-82 -
EPS(10)
E2(0) * (1+g2)
EPSI (10)
PRICE2
= (1+ g2) 10 *P1
PRICE2
P1
PRICE2
P
E2(0)
E
P
(1+g2) 10 P1
E
EPSI (10)
E2(0)
where:
E2(10)
= Earnings of Seller 10 years downstream.
ISH
= Number of shares of Purchaser issued to
buy Seller.
EPSI (10)
= Earnings per share issued of Seller in
Year 10, i. e., E2(10)/EPSI(10).
PRICE2
= Price paid to Seller.
P1
= Stock price of Purchaser,
E2(0)
= Earnings of Seller during the accounting
at time of purchase
period prior to the merger
g2
= Projected growth rate of earnings for Seller.
-83 E 1(0)
= Earnings of Purchaser during last accounting
period prior to merger.
NOS1
= Number of outstanding shares of Purchaser.
EPS 1(0) = Earnings per share of Purchaser during the
accounting period prior to the acquisition.
STDIL
= Short-term dilution in EPS.
Thus far, the question that we have answered is "How
can we make sure that what we are paying in current terms
today is consistent with what we want to receive in the future ?"
Answering this question provides us with the information we need in order to match our investment decision with
our corporate objectives.
The amount of initial dilution for accretion in EPS is
given by the formula
E1(1) + E2(1)
= EPS 11)
* (1 - STDIL)
NOS1 + ISH
But just like an initial dilution does not tell us much about the
long-term potential of recovery, similarly short-term accretion
-84-
is no guarantee that in the long run earnings will not be diluted
with respect to what they might be if no merger had taken place.
After having assumed the immediate impact on EPS of
the acquisition being considered, it becomes important to es tablish what the intermediate and long-term consequences are
going to be.
In Chapter X of a book published by the American Management Association 4 , we find a formula that allows to evaluate
the behavior of EPS over time as a function of certain assumptions on the relative P/Es and growth rate projected for the two
companies.
The formula is valid for situations where a P/E
multiple is known for both companies.
We shall first illustrate
the usefulness of the formula as it is presented, then proceed
to make it more directly applicable to the evaluation. on nonpublicly traded companies.
The formula provides an answer to the question: How long
will it take a company, whose growth rate equals or exceeds
that of the acquiring company, to cause EPS 3 to be greater than
EPS 1? Or alternatively, how long will it take a company with
lesser or equal growth prospects to cause EPS3 to be lower than
EPS 1i?
4 D.
H. Shuckett, H. J. Brown, E. J. Mock, Financing for
Growth, American Management Association, 1971, pp. 118.
-85 -
The formula, whose derivation we shall not cover,
is (making use of our own symbolism):
PE1
PE2
(l+g2)n
>
1
(1 +gl)
(4. 1)
where n is the number of years, as defined above. If we apply
this formula to the example discussed previously, we have
gl
=
8%
g2
=
12%
PE1
=
18
PE2
= 24
L
PE1
PE2
n
11 +
+glg23
.75
1
1. 037
No
2
1. 077
No
3
1. 160
No
4
1. 350
Yes
(col.
1 * col.
3) > 1?
This analysis tells us that EPS3 < EPS1 for the first three
operating years and that from the fourth year on accretion
will result.
-86-
Conversely, let us consider the hypothetical case
where the relative values of g and PE are the following:
80
g
=
g2
= 6%
PE
=
18
PE2
=
15
1 + g2 n
PE1
PE2
n
1+ gli
(col. 1 * col. 3) > 1?
1. 2
1
.99
Yes
2
. 98
Yes
3
.96
Yes
4
. 92
Yes
5
. 846
Yes
6
. 717
No
Although the acquisition of a company with somewhat lower
growth rate than the acquirer results in a beneficial contribution to earnings per share of the combined entity during
the first five years following the merger, in the sixth year
dilution ultimately occurs.
-87-
For those situations where a P/E ratio is not available
for the acquisition candidate, as in the case for a non-publicly
held firm, the above formula may be used as a tool to determine the maximum price per share, or for the whole company,
which should be paid in order for the acquirer to incur no EPS
dilution by a specified year.
Rearranging the terms of (4. 1), we
obtain the following expression for the maximum price:
PRICE2 = PE1 * E2(0) * [( +g
(1 + gl)
Alternatively, if it cannot be assumed that ear nings will grow
at annual compounded rates of G1 and G2, each year's estimated
growth rate g
t
and g2t can be introduced into the formula. For
any year n we may then express:
PRICE2 = P1 * NOS1 * E2(n) = V * E2(n)
El(n)
where V
El(n)
= present market value of the acquiring firm's equity.
In conclusion, earnings per share is a valuable criteria
to use in evaluating an acquisition.
However, it is not per se a
sound goal for expansion. We have seen that if the new invest-
ment on a present value basis earns less than the rate of return
-88-
of the acquirer's assets, earnings per share may show an immediate improvement, but will ultimately decline, and thereby
reduce the value of the firm.
The conclusion to be derived
from this result is obvious5. An acquisition must first show its
profitability through a discounted cash flow analysis; then, earnings per share may be examined. Conversely, following the
acquisition, earnings per share could drop, but if this drop is
accompanied by an overall risk reduction in the predictability
of the returns, the investors would not necessarily be worse off.
Another reason why EPS is not a valuable overall criteria is that,
just as it does not take risk explicitly into account, it says nothing about cash flows (as distinct from accounting income) available from the investment.
B.
R.O.I.
One of the most common criteria to judge any investment by is
the expected rate of return.
It has proven to be, in other capital budget-
ing decision, one of the best measures of potential profitability and its
use in evaluating acquisition is equally valuable.
The rate of return is related to the price/earnings
ratio and to
the growth rate in earnings expected from the acquisitions according to
the following equation
PRICE2 =
E2(0)
5 J.
+ g2 t
+r
F. Childs, 'Profit Goals for Management", Financial
Executive, February 1964.
-89Where PRICE2 is the price of the acquisition, E2(0) are the earnings
of the acquistion for the past twelve months, g2 is the expected growth
rate in earnings, r is the rate of return, n is the horizon year.
Graphs and tables for different values of n appear in two arti6
7
cles, one by Cunitz and the other by Fray and Ackerman . The latter
have developed a computer program which can generate sets of graphs
using any desired combination of growth rates over n years.
By enter-
ing these graphs, one can use the compounded internal growth rate and
the firm's required return on investment to determine the P/E ratio.
The maximum price is then computed by multiplying the firm's previous
year earnings by that ratio.
If the transaction is going to be of a taxable nature, and the acquisition price so determined is far in excess of the book value of the
seller, additional charges to income may have to be assumed in terms
of goodwill amortization and/or depreciation of assets restated at their
fair market value.
In this case, these charges should be computed and
the earnings figure must be readjusted to reflect the actual earnings in
the hand of purchaser.
The price to be paid for the acquisition, as computed above,
may also have to be adjusted to take into consideration the present
value of any incremental investment or divestment that may be required
in the future to achieve the assumed growth target.
6 j.
A. Cunitz, "Valuing Potential Acquisitions", Financial
Executive, April 1971, pp.
7Op. Cit.
-90-
One more adjustment may be necessary to determine the price
to be paid for the acquisition if its returns are to be consistent with the
objectives of the parent.
erage.
Specifically, we have in mind the issue of lev-
Adjustments should be made for any change in the level of fin-
ancial leverage available to the firm after the proposed acquisition. If
cash is not a scarce resource and the buyer has no intention of using
excess debt capacity, then probably no adjustment is necessary.
So far, we have referred to ROI as the DCF rate of return on
investment (i. e., internal rate of return) as may be determined from
the present value formulas. In practice, however, ROI is usually calculated in book terms, that is, as the ratio b of net income to average
invested capital or net worth during the accounting period.
Solomon 8
has shown how b and r differ, and how b is generally a complex function
not only of r but also of a firm's depreciation and expensing policies,
time configuration of assets' returns, and other items.
The implications of the differences between b and r can be sum-
marized to:
1.
For a single company, b cannot be treated as an unbiased
estimate of r.
2.
When analyzing data from several companies, one can-
not directly equate differences in b, with corresponding differences in r.
8E. Solomon, "Alternative Rate of Return Concepts and Their
Implication for Utility Regulation", The Bell Journal of Economics and
Management,
Vol. 1, No. 1 (Spring 1970), pp. 65-81.
-91-
3.
One cannot use as the required rate of return for ex-
ante investment analysis the DCF rate of return and then mea-
sure ex-post performance in terms of book rate of return.
To avoid any inconsistencies, the actual or prospective performance of an investment is measured in DCF units, and if this rate
is being measured against some standard, the relevant standard must
itself be computed in DCF units.
Therefore, in looking at other com-
panies in an industry to determine the return that investors demand
in that industry, if this figure is going to be subsequently used to perform DCF analysis, then one should make sure to focus on the market
rate of return k (the cost of capital) not the book value return.
Risk
adjustements may then be introduced to allow for perceived differences
in riskiness between the kind of investment being evaluated and the kind
of investment from which the market rate of return has been derived.
In conclusion, ROI and EPS are only two of several criteria that
management will make use of in evaluating an acquisition.
For instance,
the issue of control may at times be just as important, particularly
when the size of the seller is not negligible with respect to the size of
the buyer. If a cash transaction is envisioned, the purchasing firm
may be concerned with meeting minimum working capital needs. These
and other goals have to be traded off against one another. In Chapter VIII,
we will present a technique that, under certain assumptions, can be of
help in structuring a financial package that is consistent with the relative importance that the decision maker assigns to each goal.
-92 -
C.
Diversification
In dealing with risk, that is, with the estimated variability of
future returns, we have so far followed one of the propositions of
modern capital theory, namely,
That the risk characteristics of a capital investment opportunity
can be evaluated independently of the risk characteristics of the
firm's existing assets or other opportunities 9.
In so doing, we assumed that investors are able to achieve the same
degree of diversification as the firm is able to achieve for them (case
of perfect capital markets).
The assumption of perfect capital markets, and its conclusion
that, unless synergistic benefits accrue, conglomerate mergers consumated solely for purposes of diversification do not enhance shareholder's wealth 10 has been challenged by many authors.
In the course of this section, we will assume imperfect markets and furthermore that the companybeing acquired offers the stockholders of the acquiring company some diversification opportunity not
to be otherwise found in the market place. This may be a plausible
condition with closely-held corporations. In imperfect markets,
investors may not have the same opportunities as a corporation has.
(continued on page 94)
Stewart C. Myers and Gerald A. Pogue, A Mixed Integer
Linear Programming Model for Corporate Financial Management,
Working Paper Alfred P. Sloan School of Management.
S10.C. Myers,"Procedures for Capital Budgeting Under
Uncertainty," Industrial Management Review, Sprihg 1968.
PAGES (S) MISSING FROM ORIGINAL
-94 -
In this light, a merger represents a potential gain for investors,
es-
pecially if it is considered that on the average investors hold less than
four stocks
. It is true, however, that they account for a small frac-
tion of the total stockholdings.
An additional source of gain has been pointed by Levy and Sarnat 12:
If we assume that in any given year (or run of years) there
exists for each individual firm some positive probability of
suffering losses large enoughto induce financial failure, . ..
the joint probability of such an event is reduced by ... the
combination of other than perfectly correlated income streams
in a conglomerate merger ... The diversification can be expected to create a time economic gain to the shareholders
owing to the fact that the combination of the financial resources
of the two firms making up the merger reduces lender's risk
while combining each of the individual shares of the two companies in investors' portfolios does not.
If the firm does something for the investor that he cannot do for
himself, then this action may result in an increase in share prices.
Therefore, while theoretically, under perfect market situation, diversification by the firm should not benefit the shareholders,
in practice
it may well be a legitimate concern of the firm and a positive contribution to the wealth of the shareholders
13
.
1 J. Lintner, "Expectations, Mergers, and Equilibrium in
Purely Competitive Securities Market", American Economic Review,
May,
197 1.
12H.Levy and M. Sarnat, "Diversification Portfolio Analysis
and the Measy Case for Conglomerate Mergers", Journal of Finance,
September
13 J.
1970, pp. 801.
F. Weston, E. F. Brigham, Managerial Finance, Holt
Rinehart and Winston,
1969, pp. 229.
-95 In what follows, the risk of the prospective acquisition will be
judged in terms of its marginal contribution to the risk of the firm as
a whole. By taking this approach, the price, or alternatively, the cost
of financing the acquisition will reflect the diversification effect that
its acceptance may have on the risk inherent to the acquirer's
returns
to equity.
A favorable portfolio effect will result if the returns of the ac-
quisition vary inversely or less than exactly proportionately with those
of the acquirer.
This would tend to make the overall returns to the
firm more stable over time, and therefore, less risky.
The degree of proportionality in the variations of returns between two firms is at the basis of the statistical concept of correlation.
When the variations of returns of two firms tend to vary in the same
direction, there is said to exist positive correlation; if the variations
tend to vary in opposite directions, there exists negative correlation;
if no covariance can be established for the variations, the estimated
returns for the two firms are said to be uncorrelated.
As related to the resulting portfolio effect that the consolidation
of two firms may have, uncorrelation is not as useful for reducing over-
all risk as is negative correlation, but it is better than positive correlation.
-96 -
The returns of investments which are closely related to the
firm's basic products and markets will generally be highly correlated
to the returns of the existing assets and, therefore, will not reduce
the overall firm's risk. However, investments in other markets or
different product lines may present a lower degree of correlation with
the acquirer and thereby provide overall risk reduction to the firm.
Diversification through acquisition usually can be accomplished more
quickly and perhaps more efficiently lhan
through internal growth
alone.
In what follows, we shall illustrate methods through which management can evaluate investment proposals, taking the point of view of
improving the total business-risk
complexion of the firm.
The conceptual basis for these methods was developed by
Markowitzin 1952 and applied to stock portfolio selection
5
Therefore,
some of the probability concepts to be employed come from security
portfolio analysis. Two key relationships are the equations for port folio return and standard deviation.
i.
Portfolio Standard Deviation
The total variance of a combination of risky invest-
ments depends (i) upon the risk of each individual investment
and (ii) upon the degree of correlation between investments.
1 4 Van
15H.
Horne, op. cit, pp. 180.
Markowitz, "Portfolio Selection", Journal of Finance,
March 1952, pp. 79-91.
-97 -
In the two asset case, the standard deviation on the returns
of the portfolio can be expressed as:
ap
x2 2+(1 -x)2
a2
2
(4. 2)
where x is the proportion of the total funds invested in Investment 1 and (1 - x) is the proportion of funds invested in 2. p
is the coefficient of correlation between the two investments.
From the formula above, it appears that, on account
of the coefficient of correlation, an investment which when
considered in isolation may have the lowest risk, may in fact
not provide the lowest total variance on the returns to the firm
when it is included as part of its existing assets.
ii.
Portfolio Rate of Return
The expected rate of return on a portfolio is the weighted
average of the expected rates of return of the individual investments.
In the two assets case:
r
iii.
= xr 1 +(1-x)r
2
(4.3)
Evaluating the Acquisition
In taking the portfolio approach, one would compute the
expected return of the acquisition and its standard deviation,
-98and using Equations (4. 2) and (4. 3) compute the rp and the ap of
the portfolio that includes the acquisition as part of the firm.
For various acquisitions that are being evaluated, one can
thus select the one that has the most favorable combination
of return and risk for the firm as a whole. In Appendix D, we have
described how, in the case of isolated investments, it is possible
to eliminate the need for subjectively determining the desirability of risk-return
combinations of one investment versus
another. Tuttle and Litzenberger' 6have extended their "riskequivalence" method to the portfolio approach. The assumption
made is that management wishes to maintain the degree of risk
inherent to the returns to equity prior to the acquisition.
This may be done by trading off financial risk for
operating risk. On the assumption that the amount borrowed or
lent is considered as part of the price to be paid for the acquisition we may determine what fraction
of the total package
should consist of equity, so as to keep the financial risk to the
equity after the acquisition equal to before.
If
< 1, 1 - B
will represent the amount of debt the acquirer has to issue as
part of the payment; if
> 1,
- 1 represents the amount of
lending that must accompany the package.
16Tuttle and Litzenberger, op. cit., pp. 435 ff.
-99Let:
a l(t) = estimated standard deviation (or error of return) on
the acquirer's
equity at time t (t = 0 prior to the ac-
quisition; t = 1 after the acquisition).
= estimated standard deviation of return on the total
a2
equity of the acquired firm after the acquisition.
= estimated standard deviation of the acquisition can-
02
didate's
V
ROA (12).
= the market value of the firm's equity, pre-acquisition
1
PRICE2 = price to be paid for the acquisition
= proportion of total equity funds to be invested in the
o
acquisition (CSI/V1 + CSI).
(1 - o
)
= proportion of total equity funds invested in the original
firm.
P
= coefficient of correlation of the returns from the acquisition with the returns on the firm's existing assets.
Then the o can be expressed as
p
It
crp =
o
2
tO)2
(CT)2
"-,1
+
2
p
W0(1
- W0
a
J
2 aI
(4. 4)
-
-100-
Since by definition
w
* PRICE2
o
V1 + 3 * PRICE2
and
E 2 +D
*
2
1
2
2
3
E2
we may rewrite (1) in terms of
2
PRICE2
a*(1)
1
V1
02
PRICE2/
+a
I .~
I
+ 2p
2
II I
2
as:
V1
+
\V1 +
2
* PRICE2 I
,
,-_IA
..
I .I..
'*1"V"
I
PRICE2 * V1 ' o1(0) 02
(V1 + 3 * PRICE2)
(4. 5)
Since we want to determine the value of 3such that the risk
to the acquirer's
a 1( 1)
1
=
equity may remain constant, i. e.,
(0)
1~~~~~-i
1
(4. 6)
we equate the two expressions and obtain the following quadratic equation in
1:
-101(PRICE2 * o (0))2 f2 + 2(V1 * PRICE2 * 1(0))2 3
- PRICE2 *
2
(PRICE *
2
+ 2p V1 * o1(0)) = 0 (4. 7)
Once this equation is solved, the cost of financing the
acquisition is simply:
k =
* 2 + (1 - 3)i
where p2 represents the expected return on equity of the acquisition, and i, the riskless interest rate.
This is the risk-
equivalent cost of capital as used in Appendix C and 3 and (1-3),
as computed by solving Equation (4. 7), are the appropriate
weights to be used in financing the investment, if 12 is to remain
unchanged. The acceptance of the acquisition candidate can then
be determined by discounting its expected cash flows by the cost
of financing k and applying the net present value (NPV) criterion
to the discounted stream of net cash flows. In equilibrium, the
aggregated increase in the market value of the firm's previously
outstanding common equity would equal the acquisition's NPV
when discounted by its cost of financing. Such is the case here
since under the hypothesized market conditions the estimated
standard error of return to equity and, hence, the equity capitalization rate, will remain unchanged.
It is often the case that the mix of funds to be used to
pay for the acquisition is known. In such cases, Equation (4. 7)
-102-
can be solved for PRICE2, the price to be paid for the acquisition given that the acquirer wishes to preserve the amount
of risk inherent to the equity prior to the acquisition.
In practice, when several prospective acquisitions are
being evaluated, one must first describe each acquisition in
terms of its t and a. Then one must compute the p and p
given that each acquisition is now part of the acquiring firm.
The resulting
p
and ap
of the several portfolios may then
be plotted on a scatter diagram, as depicted below.
a
'3
2
'A
Figure 4-1
-103-
Collectively, the points represent the total set of investment
opportunities available to the firm.
Certain dots dominate
others in the sense that they display a higher rp for the name
O ( dots 5, 1) or a lower a and the same r (5, 3) or both a
higher rp and lower ap (5, 2). Therefore,
4 and 5 dominate
all others, but it is not possible simply by inspection to decide
which of the two projects is more desirable.
Using the Tuttle-
Litzenberger technique, we make the internal rate of return
on those two projects risk-equivalent to the firm's equity of
borrowing or lending. We then select that acquisition which
produces the highest return.
We conclude the section by restating the fact that the
acquisition of a privately owned company with a low degree of
correlation withthe existing operations of the acquirer provides
a firm with the possibility to reduce its overall business risk
complexion, and hence, increase the market value of its equity.
Though this concept is theoretically quite powerful, we realize
that in practice the quantitative analysis may be rather difficult
to perform.
-104CHAPTER
V
Forms of Payment
One of the many financial issues to be addressed in the analysis
of an acquistion candidate concerns the exchange terms and media to be
employed in the transaction.
Specifically, it is necessary to determine
the form of the transaction and the type and amounts of securities to be
exchanged, which will most satisfy the diverse interests of the buying
and selling stockholders. In the present chapter, we will first briefly
discuss the various forms of transaction along with some of the advantages and disadvantages of each. We will then explore the implications
that taxes may have on the price that the buyer is willing to pay for the
firm, depending on the form of payment.
Finally, we will concentrate
on one particular type of merger financing tool, the contingent payment
contract, because it has proven particularly attractive in the acquisition
of closely held corporations. In consideration of the differences that
may separate the buyer from the seller with respect to the value of the
firm, this type of contract will be introduced as a logical way to
bridge these differences and reduce the perception of risk involved in
the acquisition.
-105A.
Type of Transaction:
Purchase and Reorganization
There are various possible methods that may be used in acquiring a business and each has different attractiveness to the seller and to
the buyer.
The various media of payment that can be used in isolation
or in combination include: cash, bonds, preferred stock, common
stock, warrants or convertibles.
There are two basic types of transactions that are used to combine business entities: purchase and reorganization.
The accounting
treatment of these transactions is particularly relevant to the tax as pects of a merger. A tax-free transaction, a reorganization, usually
makes use of pooling of interest accounting, whereas a taxable transaction, a purchase usually implies purchase accounting.
Under a pooling of interest,
all assets of the newly combined
group are valued at the same amount at which they were previously
carried in the accounts of the individual firms.
Under the purchase
method, the buying company is permitted to write-up the value of the
acquired assets to reflect the purchase price. The excess of the purchase price over the assets acquired is called goodwill. Goodwill is
recorded as an asset and amortized over a number of years not to exceed 40, as specified in the Accounting Principles Board, Opinion 17.
This amortization cannot be expensed for tax purposes but is nevertheless charged against income and, therefore, has a negative effect on
earnings per share, without providing a compensating benefit through
tax shelter.
-106-
Let us now consider the various forms of purchase and reorganization, along with some of the advantages and disadvantages of each.
1.
Purchase
This type of transaction is usually treated as taxable. The
shareholders of the selling company are subject to immediate payment
of capital gains tax based on the difference between the acquisition price
and their original cost basis.
i.
The more relevant forms of purchase are:
Purchase of Assets
In a purchase of assets, the seller may be double-taxed
both at the corporate and the personal level unless (i) the seller
adopts a plan for liquidation under Section 336 which avoids taxation at the corporate level, or (ii) a corporation is formed to
buy at least 80 percent of the stock, which is then liquidated
within two years.
Another problem is the allocation of the purchase price
to the various assets 1
From the buyer's point of view, tax-loss carry-overs
cannot be bought as an asset.
Also, it may be difficult to obtain
certain leases or franchises.
1Allen D. Choka, Buying, Selling and Merging Businesses,
Business Associations/Practice Handbook, 1965.
-107-
ii.
Purchase of Stock
The most common problem to the buyer is that of un-
foreseen liabilities; the buyer can partially hedge by using an
escrowagreement.
Also, assets cannot be written up, unless
liquidation is used.
iii.
Installment Purchase
The tax-law allows profits from the sale of property
to be reported in the years in which payments are received,
both for purchase of assets or purchase of stock, provided
that the payment received during the year of sale is not in ex-
cess of 30 percent of the total selling price.
This method may be of interest in buying a closely held
corporation, because the owners can either save taxes, depend-
ing on their tax bracket, or can defray taxes to future years,
when each additional payment is received.
2.
Reorganization
This type of transaction usually qualifies for tax-free treatment:
the shareholders of the selling company are thereby allowed to defer
payment of capital gains tax on the newly received shares until the time
these shares are sold.
The more relevant forms of non-taxable transactions are:
-108-
i.
Type A
This includes the consolidation, whereby two corpora-
tions are fused into a new third entity, and the statutory merger,
whereby one company becomes part of another which is the surviving one.
These are the only forms of reorganization in which the
stock issued does not have to be voting stock. In fact, cash or
debt may be used as part of the payment, if the seller pays ordinary taxes on it, and if the stock portion is at least 50 percent
of the total exchange package.
ii.
Type B: Stock for Stock
Only voting stock is exchanged for at least 80 percent of
each class of voting stock of the acquired corporation.
This
method is particularly popular when a listed company is buying
a closely held corporation, because it affords the seller liquidity
and flexibility.
The disadvantage to the buyer, a part from dilution
problems, is that tax-loss carry-overs
cannot be used in as
much as the corporate entity of the acquired company remains
alive.
This tax-loss carry-over can be used only if the com-
pany turns profitable or a subsequent reorganization to a new
A or C type occurs.
- 109-
iii.
Type C: Stock for Assets
Only voting stock is exchanged for substantially all the
assets of the acquired corporation, where "substantially all"
test is believed to be about 80 percent of the market value of
the assets.
This technique is often selected in order to avoid ac-
quiring certain assets or assuming certain knownor any unknown liabilities.
For a more complete treatment of this subject, a valuable reference is: Schuckett, Brown, Mock "Financing for Growth", American Management Association, 1971, Chapter 16.
-110-
B.
Tax Implications in Merger Negotiations
Taxes may largely determine the preferences for a particular
type and form of payment. For instance, buyers may be interested in
taking advantage of tax-loss carry-forward
of firms who have had con-
siderable losses in most recent years of operation. The buyer can only
take advantage of these losses if it owns at least 80 percent of the acquired firm's voting stock. A seller, on the other hand, may be inter-
ested in deferring his tax consequences, in minimizing estate taxes, or
in avoiding double taxation.
If no tax considerations were involved,
whether the transaction is ultimately going to be accounted for as a
purchase or as a pooling of interest would not affect the valuation of
the acquisition. Whentaxes are taken into consideration, the accounting mode of acquisition can no longer be overlooked.
Generally speaking, an acquisition, when treated as a purchase,
allows the buying company to amortize depreciable facilities and thereby provides a tax shelter that depends on the extent of the assets writeup. The greater the differential between the acquisition price and the
book value of the acquired company, the greater the benefit to the buyer.
Because a stock acquisition does not provide this advantage, the buyer
is usually willing to pay a higher price for a cash transaction than for a
stock transaction.
To the seller exactly the opposite is true: usually a stock trans action is preferable,
due to the opportunity it provides to defer payment
-111-
of capital gains tax. Therefore, the analysis of the tax consequences
of the acquisition centers around the issue of whether the incremental
benefit to the buyer provided by the stepped-up basis is large enough
to allow compensating the seller for the additional tax costs that he
would incur, and yet still provide a residual benefit to the buyer.
Schwartz 2 illustrates this point through the following example:
Tax-Free
Taxable
Taxable
Sales Price
30
34
31. 3
Estimated Cost
Basis
22
22
22
8
12
Capital Gains
Capital Gains
Tax, 25%
2
(paid in 10th year)
3
(paid now)
9. 3
2. 3
(paid now)
Present Worth of
Tax at 8%
1
3
2. 3
Net Realization:
7
9
7. 0
Sales Price Less
Present Worth Af
29
31
29
Capital Gains T
The price to be paid for the acquisition, subject to a tax-free transaction, is assumed to be $30, 000, 000 and the same price on a taxable
basis is assumed to be $34, 000, 000, reflecting a present worth of
$4, 000, 000 for the difference in tax basis to the buyer. Working through
2S. Schwartz, Merger Analysis as a Capital Budgeting Problem.
The Corporate Merger, W. W. Alberto and J. E. Segall, Univ. of
Chicago Press, 1966.
-112-
the tax implications to the seller, the latter turns out to be better off
by $2, 000, 000 under a taxable transaction.
If the seller,
however,
were paid $31, 300. 000, he would be as well of in a taxable acquisition
as in a tax-free one. Therefore, a settlement in the price range between $3 1, 300, 000 and $34, 000, 000 for a taxable merger is beneficial
to both the buyer and the seller.
In a following chapter, we will be discussing a technique that
allows the buyer to evaluate different ways of structuring a merger
package so as to best satisfy his company's internal goals. Many of
the constraints that the buying company must satisfy come, however,
from the need to cater to external goals, those of the seller.
Some
sellers are looking for a good cash flow in the years following the sale.
Others want nothing but capital gains. Some need cash to start a new
venture, others cannot bear the thought of paying taxes.
Some are
looking for a continuation of their involvement in the management of
the firm, others are looking for ways to pass on the largest possible
share of their wealth to their heirs.
Both parties are subject to a mixture of influences which are
both personal and corporate, private and public. Structuring the appropriate deal is oftentimes a creative step and imagination may well
be an essential prerequisite to closing a deal, particularly when the
seller is a privately-held concern.
I
-113-
C.
The Contingent Contract
The difficulty inherent in the valuation process, differences in
goals and expectations, the limitations of the techniques available to
deal with the uncertainties involved, undoubtedly all contribute to the
gap in expectations that usually separates the buyers from the sellers
with respect to the price to be paid for an acquisition.
Expectations can be particularly divergent when the selling company does not possess a complete history of operations, or has only
been in existence a short while, or where there is considerable doubt
about its ability to perform after the acquisition. This is especially
true for closely-held corporations, when records may be incomplete
or unaudited, or where the seller may feel that he has made no attempt
to get the best out of the firm.
In fact, he may contend that he has tried
harder to keep the earnings low, rather than maximize them. As a re-
sult, the seller may feel that current and past reports understate the
true potential of his firm.
The question is then, what if anything can be
done to narrow the gap between the buyer and seller.
When the seller
is willing to continue managing the firm, the use of contingent payment
contracts (also referred to as earn-outs, buy-out plans, contingent payouts) has been suggested
3
as a logical way to reconcile, from a business
point of view, positions that look otherwise quite far apart.
3 C.
1967.
Hecht, "Earnouts", Mergers and Acquisitions, Summer
-114-
A contingent payment plan implies that the price paid for the
firm, will be determined in part at least by the performance of the acquired firm after the acquisition.
The down payment by the buyer can be made in any of the forms
discussed in the previous section.
The lower the down payment, the
greater the upside leverage and the downside protection to the buyer,
the greater the risk to the seller. The buyer also agrees to additional
payments if the seller meets or exceeds predetermined performance
standards during a certain number of years following the acquisition.
Contingencies can be based on sales, net worth, market values, cash
flows, return on operating assets as well as earnings which is the most
common criterion. The only real limitation to the selection of the criterion is that it be measurable.
1.
Contract Types
Various formulas have been developed to link the payment
scheme to the performance criteria.
is the "set standard
"4
The most commonly used contract
of the "base-period earn-out".
Contingent pay-
ments are made during each year in proportion to the amount of increase
in earnings in excess of the base year's earnings. The seller receives
either a cash payment at some multiple of those excess earnings, or if
stock is the medium of transaction a number of shares equal to:
4 W.
Reum and T. Steel, "Contingent Payouts Cut Acquisition
Risks", Harvard Business Review, March-April, 1970.
-115-
excess earnings * capitalization rate
market price
Where the denominator represents the market price of the shares of
the buyer's common stock and the capitalization rate, subject to negotiation, is the multiplier (a number) that is applied to the excess
earnings.
A second type is the "moving standard" of the "increment earnout ". This method emphasizes continuous growth and prevents the
seller from fluctuating earnings in order to increase the payment. The
standard is the previous year's earnings, but normally the agreement
will also state that the highest earnings in any of the previous earn-out
years must be used. This way the seller is not allowed to take advantage of a bad year, which would tend to make the following year's improvement look artificially high. The expression that can be used is
similar to the base year formula:
yearly increase in earnings x capitalization rate
market price
The "cumulative earn-out" focuses on cumulative earnings per-
formance. Current earnings are multiplied by the number of years in
the contract period and this is used as a standard against which to compare the earnings at the end of the contract period.
This method focuses
-116-
on the whole period and no shares, unless otherwise agreed, will be
received by the seller till the end of the period.
Finally, the "reverse earn-out" essentially reduces the purchase
price, which is originally paid in full, ifperformance is not met.
Whatever
the contract type, the buyer and seller have to nego-
tiate
an appropriate standard and the reward function. The buyer
usually sets a maximum on the number of shares to be paid out in any
one period to prevent excessive dilution of earnings.
Accountingprocedures for contingent contracts are discussed
in detail by S. P. Gunther.
2.
Advantages and Disadvantages
The major conceptual advantage of using this type of merger
financing is that it offers the possibility of reconciling positions with
respect to the valuation of the firm, that might otherwise be totally
opposite.
In fact, it removes many of the pressures of dealing with
the uncertainties involved in setting a fair market price, by allowing
the final price to be determined on the basis of performance. For the
seller, it provides a chance to prove the real worth of his business
and fully capitalize on it.
Other advantages to the buyer include:
5S.P. Gunther, "Contingent Payouts in Mergers and Acquisitions, " The Journal of Accountancy, June 1968.
-117-
Provides incentive to the seller's management team to
1.
stay and increase the earnings of the company.
Reduces risk, since the buyer pays for proven perfor-
2.
mance.
Effectively the buyer is borrowing money from the seller
3.
to finance the acquisition.
Reduces the impact of dilution, although opinion 15 of
4.
the AccountingPrinciples Board now requires that earnings per
share be reported on a fully diluted basis.
One of the major disadvantages is that the contract must be negotiated
in every detail.
in general.
This includes defining earnings and accounting practices
There are many ways in which earnings may be manipulated 6
and care must be used to avoid problems connected with depreciation,
capital budgeting, discretionary expenditures and management salaries.
Other disadvantages include:
1.
Buyer is not free to reorganize; the acquired business
must continue to operate as an autonomous subsidiary.
2.
Seller suffers a delay in receiving his full payment and
thereby bears a share of the risk.
3.
The contract must be administered during the contingent
period.
6 "What Are
May 15, 1967.
Earnings?
The Growing Credibility Gap", Forbes,
-118-
4.
The seller may be tempted to sacrifice long-term
profits for short-term gains.
-119CHAPTER VI
Acquisition Analysis: A Procedural Framework
Thus far, we have described several concepts and methods
which may be of use to the valuation of a closely-held firm.
Some
techniques were presented because of their widespread use in the field
or because they were found applicable to perform a specific calculation;
others, because they provided useful conceptual guidelines to the valua-
tion process.
In this chapter, we propose a framework of analysis that draws
on a subset of these techniques and which suggests a practical procedu-
ure for performing the valuation analysis of a prospective acquisition.
Because all the concepts which are used in this chapter have already
been presented in previous ones, we shall assume the reader is reasonably familiar with them, and shall, therefore, not indulge in further
elucidations. Furthermore, for purposes of clarity, we have deemed
it advantageous to present the proposed framework by means of flowcharts rather than through a verbal description.
reader keep referring to Macro-Flowchart
We suggest the
1 as we describe the main
conceptual flow.
The basic characteristic of the framework is that it is intended
to be used iteratively and not in a "one pass" mode. That is, the
-120-
acquirer should start going through its procedural steps as soon as
he has enough data to work through each step. He thereby obtains
an initial rough estimate of the price range to be paid for the acqui-
sition. Subsequently, as he acquires more information and refines
his estimates, it will be necessary to rerun the analysis to obtain
sharpened figures and to define more precisely the range of possible
negotiating prices.
Furthermore,
at any point in the analysis, the
same interative process will be required to provide answers to any
"what if" type questions the acquirer may wish to ask.
The analysis begins with the determination of the fair market
value of the firm to be acquired.
For this purpose, we employ the
three valuation methods described in Chapter II: the asset, market
(Flowchart 2) and DCF (Flowchart 3) valuation methods.
This analysis
determines a range of possible values, lower bounded by the liquidation
value of the firm.
The next step in the analysis is to establish the value that the
acquisition has to the buyer (Flowchart 4). This is done by evaluating
the incremental benefits expected to accrue because of the consolidation
as suggested by the analysis. covered in Chapter III, Section B. The
present value of these benefits is added to the fair market value to
obtain the value of the firm before adjustments.
Two types of adjustments are then performed to determine
the maximum price to be offered for the acquisition; the first, takes
-121into consideration the tax benefits which may result from the type
of transaction used (we discuss these in Chapter V, Section B); the
second computes the price constraints set by various performance
criteria as discussed in Chapter IV (Flowchart 5).
At this point of the analysis, FUSION (as described in Chapter
IX) becomes a useful tool to evaluate, vis-a-vis specified performance criteria,
the tax advantages which may be derived by issuing
different exchange packages.
This is done by first examining the tax
benefits which may derive from the use of different types of exchange
media, and then, by using FUSION to examine, for each different case,
how close the viable packages come to satisfying the set of performance
criteria.
The result of this analysis not only determines the most at-
tractive package to be issued, but also bounds the maximum price to
be offered for the selling firm.
We denote this price as the maximum
price after adjustments and taxes (MAXPTA).
At this point in time, the analysis focuses on the seller's
pectations.
ex-
The type of transaction used has an impact on the amount
of money the seller will ultimately obtain, after taxes. The seller will
therefore adjust his demands according to whether the deal is going to
be tax-free or taxable.
In the case of a tax-free transaction,
the net
dollar amount in the hands of the seller, assuming he decides to sell
the stock in year n, will be:
NET PRICE
= PRICE2 - (PRICE2 - COST)
CGT
(1 + k)n
- 122-
where PRICE2 is the final negotiated price, COST is the taxable cost
basis for the seller, and CGT is the capital gains tax rate.
The second
term on the right-hand side of the equation represents the present value
of the capital gains taxes paid in year n.
In the case of a taxable transaction (the seller pays capital gains
taxes immediately after sale), the net dollar amount in the hands ofthe
seller will be:
NET PRICE' = PRICE2 - (PRICE2 - COST) CGT
To the extent that,
NET PRICE'
< NET PRICE
the price which would have to be offered to the seller in a taxable
transaction,
and which would yield an after-tax value equal to NET
PRICE is:
PRICE2'
=
1
PRICE2
1 - CGT
COST * CGT
_ (PRICE2
- COST)CGT
(1 + k)n
-123-
The negotiating sessions usually begin with the buyer willing
to offer at most his initial estimate of the maximum price after adjustments and taxes (MAXPTA), and the seller demanding at least
PRICE2 in a non-taxable transaction,
or PRICE2' in a taxable one.
The series of negotiation rounds which normally take place provide
the acquirer with the necessary information to reiterate through the
proposed procedural framework and obtain updated values for MAXPTA. If we let MINBT denote PRICE2 or PRICE2', whichever applies,
the following three cases may finally apply:
i.
MAXPTA = MINBT, the deal goes through and the
negotiated PRICE = MAXPTA = MINBT.
ii.
MAXPTA > MINBT, the deal goes through and the
negotiated price will be somewhere in between those two values.
Exactly where it settles, depends on the negotiating power of
each party.
iii.
MAXPTA < MINBT, either no deal, or it may be
feasible to work out a contingent payment contract as des cribed in Chapter V, Section C.
-124-
Flowchart
1
ysis
LI
Q:b
oLU
>.
c
3
I
FUSION
PROGRAM
- 125 -
- - - - -
COMPUTE FINANCIAL AND
- - - - *
- - - - I- Performance
criteria:
OPERATING PERFORMANCE
FIGURES FOR FIRM TO BE
I ROA: time weighted average
I
I
I
I
use boxes 2 and 5 in F lw. 5
I GROWTH:
ACQUIRED
I
I
I
I
r2
PROFIT QUALITY: compute
riSOLVENCY:( + /E
LIQUIDITY current assets
current liabilities
I
I
I LIQUIDITY:
I DUSTRY
I CONSTRUCT
t
W
IAVERAGES
=
I DETERI
....
i
i
-1
........
_
L,
IINE
;
I[
I
Use available statistics
I . Perform the analysis from actual
I
__
_o_perating
_
.
I,
I ADJUSTED P/E
-
--- I
_
data
_ _
_
-'I PEf
rW
PEi
I
_ _ _ _ _ _ _ _- _ _- _
ROAf
+w
Gf
2
ROAi
_I
i
I
n=l
I
2
rf
I --+__- _ __
I UMUIL- L
I,
v
EARNINGS
TAEf
_
TAE.
_ _
+ W5
_
_
,,]
CRI
rTime-weighted average of last three 1
I_fiscal years
/
.....
COMPUTE FIRM
VALUE
_
-r. +3
_ _ _
i VALUE1 = P/E * El
_
1
Flowchart
2
Market Valuation: Adjusted P/E Method
…
f
-126-
FORECAST
FUTURE
I
EARNINGS
I
I
I FORECAST
FUTURE
FrProformaforecasts using high, medium,- low estimates
I
V
I
EBIT (1 - Tc ) + Depreciation
' + other non cash charges - AWC
- A cpital expenditures
CASH] FLOW
----.-
I n
..
I
\
-
.rTTTPT
/TF0
TERMINAL
- See Table I
V
VA LUE
I
I
C OMP UTE
DISCOUNT
i Risk adjusted discount rate r
4
RATE
a
I
TV
COMPU'IE
PRESENT
rv
r
T
_
I
ITT
b
t
VALUE
I
lej
VA LUE3
!
-
-
I
-T-31
I High,
v
I\
Flowchart
Market Valuation:
`~~~~~~
T
At
-
-
-
L (1+r)t
-tr)
-
TER VALUE
(
)
medium, low value estimates
3
Discounted Cashflow
1
-127-
EXCESS DEBT-
ICAPACITY
j PV at riskless rate of after tax interest
I,
I
L payments onA_debt that can be issued
I
-
EXCESS
J
IASSETS
.
rate of (i
i
i-
c
seller buyer
J"~~~~
@ a utoi
- -I * amount of financ inganticipated
CHARGES
-ROI
BETTER
t
ADDITIONAL
INVESTMENTS
1]
L-P
-
i (ROIacquisition - ROIinternal)
I_*_anticipated invest in acquisition - - - -
0
USE OF
FUNDS
II
NI NPV at cost of capital of stream of cash -I
I flows after taxes_generated byinvestments ,
I Incremental price paid for having firm in
TION
DIVERSIFICA
---
Ih
'-
--
value of excess assets I
PV at riskless
LOWER
FINANCING
I
__,Liquidation
ver cnsderng
t n satn
ithe portfolio over considering it in isolation,
~ P~q
r
I
.UIV'
BENU
L
PVBEN
IN
-j I
I
4I-
FAIR
MARKE
VALUE
f
overall benefits
,;i'
. MAX PRICE
BEE ADJUST.
.
I
Flowchart
4
Value to Buyer: PV of Benefits
I
- 1281
I Earnings = net income to shareholders
4 before efd div. after interest
OBTAIN EARNINGS
HISTORY TO BE USED
AS INDICATORS OF
I
I
PAST GROWTH PATTERN
.
2
_
_
COMPUTE INFLATION
-Index number for final year -
INDEX DURING THE
GROWTH
3
.L
COMPUTE TOTAL
DEFLATED, COMPOUNDED
I
for first year
Index number
PERIOD OF EARNINGS
ANNUAL GROWTH
I Index number for GNP implicit price
I
I
I deflator
I
I Last year earnings
"I First year earnings
I Total growth
I Inflation index
=
== frtaI
ar -r-t
pact
h
... b
deflated growth
I
I
I
I Deflated growth table> compound growth I
PORTION OF GROWTH
FROM INTERNAL FUNDS:
COMPUTE
I Increase in R.E. + reserves
I Increase in NET WORTH _
CHANGE IN
SHAREHOLDERS' EQUITY
DURING THE PERIOD
I
1
5
I COMPUTED ADJUSTED
I
= y%
_ _
_
ROWTH RATE
1 Given G and ROI compute P/E
6
SPECIFY~ COMPUTE P/E
RATIO
ROI
I
~L----
C_ompound
annual growthrate * LY)_
m
P/E
t
=
11+ROI
7
I VALUE
-
-~~~~~~~
4
-
Flowchart
Market Valuation:
IPJ/E_
E_2C)_ =
5
ROI Approach
Value 4_ _ _
ratio:
I
- 12 9-
CHAPTER VII
Structuring the Merger Package
In Chapter V, we have argued how it is necessary to determine
the purchase price and the types and amounts of securities to be exchanged, which will most effectively satisfy the diverse interests of
the buying and selling stockholders.
This requires that the pricing
and packaging analysis be performed in the light of both its impact on
the parent and candidate stockholders and on the corporation's capital
structure and long-range plans.
In general, the acquisition staff performing such analysis has
only a vague idea of what price and exchange package would be attractive to both organizations.
Hence, several combinations need to
be explored before a recommendation is made to top management. This
trial and error way of proceeding, whether performed with the aid of a
computer or not, can turn out to be quite lengthy and expensive.
To
partly shorten and facilities this task, we have used goal programming
as a technique for specifying the price and package to be used. Before
proceeding to formulate how goal programming may be applied to package structuring analysis, it will be useful to point out what the potential
applications and limitations of our implementation are.
On the applications side, the technique may be used to:
-130-
a.
Determine in a "one shot" fashion (i. e., no trails are
performed) the price to be paid and the mix of securities in the
package which most clearly satisfy the following management
goals:
i.
Issue a package of value as close to a prespeci-
fied price.
ii.
Incur EPS dilution not exceeding a specified
percentage.
iii.
Preserve a specified degree of control over the
combined entity.
iv.
Maintain a determined capital structure.
v.
Continue to pay a given dollar amount of dividends
on all shares outstanding.
vi.
Have EPS reach a specified target by a given
year -end.
b.
Determine the price to offer given that management wishes
to meet the aforementioned goals (ii) through (vi) as closely as
possible.
The shortcomings of our formulation include the following:
a.
The price of the acquirer's
shares is exogenous to the
formulation, and therefore, unaffected by the amount and types
of securities issued.
-13 1-
b.
The price to be paid for the acquisition is independent
from the types of securities used in the transaction package.
c.
The size of the prospective acquisition has to be small
relative to the acquirer.
Let us now briefly dwell with the nature of goal programming.
A.
The Nature of Goal Programming
Developed and extended by A. Charnes,
W. W. Cooper and Yuji
Ijiri , goal programming is a special type of linear programming, which
distinguishes itself in the manner goals (i. e., management desires) and
constraints (i. e., environmental conditions under which management
makes its decisions) are treated.
In ordinary linear programming, only
one goal is incorporated into the objective function to be maximized or
minimized.
If management has multiple goals, then the goals not in-
corporated into the objective function are treated as constraints of the
problem.
The computational technique then picks from the set of all
solutions that satisfy the constraints the one (or ones) that maximizes
or minimizes the objective function. Because management is striving
for the highest value of the objective function, it can be viewed as adopting an optimizing behavior.
In goal programming, all goals, whether
one or many, whether compatible or conflicting, are incorporated into
the objective function, and only the true environmental conditions are
treated as constraints.
Each goal can be set at a value judged
1The basic references on goal programming are the following:
A. Charnes and W. W. Cooper, Management Models and Industrial
Applications of Linear Programming (New York, John Wiley and Sons,
Inc. 1961) pp. 219 ff; and Y. Ijiri,
Management Goal and Accounlting
for Control (Amsterdam: North-Holland Publishing Co., 1965)
- 132-
satisfactory by management, and not necessarily representing the best
attainable value. Furthermore, management may rank its various
goals so as to obtain a solution which respects its scale of priorities.
The computational procedure then picks from the set of all solutions
which satisfy the constraints the one (or ones) that attains or comes
closest to fulfilling management's specified targets.
These differences between goal and linear programming render
goal programming a more appropriate technique when a problem involves
or calls for:
a.
The coordination of activities within a firm.
b.
A "satisfactory" rather than an optional solution.
c.
The incorporation of several goals into the solution.
The process of formulation a goal programming problem involves
performing the same initial steps that are required in linear programming. The main difference stems
from the way in which goals are
treated and expressed into mathematical equialities.
For illustration purposes, consider the simple one-period situation where a manager is faced with a short-term financing problem of
determining how much of a raw material purchase price P to pay with
cash (X1) and how much to pay by making use of a credit line (X2) bearing a 10 percent annual interest cost, and requiring him to maintain a
minimum working capital balance of $WC.
-133-
Furthermore,
assume that the manager wishes to maintain at
all times a minimum cash balance of at least $CASH. If CASH0 and
WCo represent the initial amounts of cash and of working capital, the
problem can be formulated as a linear programming problem where
the objective is to minimize the cost of financing, i. e. the cost of making use of the credit line. Since X2 denotes the amount of borrowed
dollars, we may express the objective function as:
Minimize Z = . 10 * X2
The constraints to the problem can, in turn, be formulated as
follows:
i.
The sum of the cash X 1 used and the borrowed funds X2
must equal the price P to be paid:
X1 + X2 = P
ii.
Since a minimum working capital (current assets minus
current liabilities) equal to $WC must be maintained, we must
ensure that:
WC
l-x
- X 1 - X2~ > WC
or rearranging terms,
2
-134X 1 + X2
iii.
WC o - WC
The manager wishes to maintain a cash balance of at
least $CASH. Therefore, the amount of cash X 1 used should,
at most, equal that amount which would deplete the present
balance of $CASHoto its minimum allowable level, i. e.:
CASH
- X1 > CASH
or
X 1 < CASH
- CASH
The first two constraints can be considered as externally imposed and, therefore, as "hard" constraints.
The third one, however,
represents one of the manager's goals and, therefore,
is not necessar-
ily as constraining as the others. "Straight" linear programming treats
all constraints equally and by so doing fails to provide a means of dis criminating between "hard" and "soft" constraints.
Goal programming
resolves this problem by introducing into the soft constraint (cash balance goal) surplus variable y, to represent any excess over target
amount of cash, and slack variable y , to denote any shortage from target. These two variables are defined as:
-135y
+
y
y
* y
= 0
+ y
> 0
-y
= X1 - CASH + CASH
According to this definition, at least one of the y's must be
zero, both of them must be non-negative, and their difference measures the dollar value by which the ending cash balance exceed
(y
> O and y
= O) or is shart of (y
=
and y
> 0) the speci-
fied target ($CASH).
With the variables y and y thus defined, the problem can now
be formulated as a goal programming one by attributing a cost c to
each dollar of negative
*
(cash balance shortage) deviation and by ex-
pressing the objective function to minimize as:
Minimize Z = . 10 * X 2 + c * y
To solve this problem by the simplex method, the other co
straints need to be converted into a set of equations by introducing
slack, surplus and artificial variables wherever necessary. If this
is done, the formulation becomes:
The fact that no penalty is attached to y reflects the fact
that the manager is indifferent to having an excess-over-target cash
balance.
Minimize Z = . 10 *X
2
- 136+C* y
subject to:
=
X1 + X 2 + X3
+ y
X1
xiJ y,
=WC
+ x4
X1 + X2
y
> 0
p
(i
= CASH
- W
- CASH
= 1, 2, 3, 4)
In those situations in which management has several goals,
some of which are given absolute priority over or relative to others,
the objective function to be minimized will consist of the penaltyweighted summation of each deviation to its respective target.
-137-
B.
Goal Programming Applied to Merger Packaging Analysis
Having dwelled to some extent on the nature and potential use
of goal programming, let us now explore its applicability to merger
packaging analysis by considering a situation involving the possible
use of common stock, bonds and convertible preferred as transaction
media. Also, let us assume that the acquisition transaction will take
place on January first of Year 1, and that financial projections for both
companies (as separate entities) extending five years into the future are
available.
Of the many goals that a company might wish to achieve and
which may influence the structure of the transaction package, we have
considered the following in our analysis:
i.
To incur an initial EPS dilution not exceeding a speci-
fied percentage.
ii.
To maintain a specified percentage ownership (control)
of the combined company immediately after the consummation
of the merger.
iii.
To maintain a given debt-to-equity ratio.
iv.
To attain a target EPS level by a specified Year N.
v.
To maintain a minimum working capital balance
(liquidity). This goal encompasses the goal of continuing to
pay a dividend stream of $d per share (on all the shares outstanding after the acquisition).
-138-
For purposes of simplifying and making feasible our approach,
we have made a series of assumptions.
Firstly, for reasons which
are made clear later, we have assumed that the size of the acquirer,
as measured by the market value of its equity, is much larger than
the seller's.
This assumption, in turn, allows us to make a second important
simplification, namely, that the acquirer's
common stock price will
not vary with the size and composition of the issued package. Without
this simplifying assumption, a few of the constraints become nonlinear,
and it is no longer possible to approach the packaging problem through
linear or goal programming.
Thirdly, we have assumed that the total price to pay for the acquisition will not vary with the types and amounts of securities issued
as payment. To do otherwise, brings in several complications.
Fourthly, we have assumed that problems connected with the
debt maturity and with the timing of the issue may be ignored.
Given these assumptions, the objective is to determine the package which minimizes the penalty-weighted sum of the deviations which
may result from management's specified goals.
In order to formulate the packaging problem in terms of goal
programming, it is necessary (i) to express each of management's goals
as linear equations of the securities which may enter the package, and
(ii) to find for each goal a way of penalizing any deviations which may
- 139-
result from management's specified target. In what follows, we shall
do this for each goal. Let us first, however, formulate the equation
governing the amounts of securities which may be used.
-140 -
1.
Transaction Constraint
The central constraint of the packaging problem is that the total
value of the securities issued must equal the price to be paid for the
acquisition.
Using our own symbolism (see Appendix A) and some ele-
ments of FORTRAN notation, we may express this as:
CSI + B(0) + CP(0) = PRICE2
This equation may be viewed a priori as a "hard" constraint. However,
to increase the potential uses of the proposed packaging technique, we
have added surplus variable Y+ to denote any discount over PRICE2
and slack variable Y to represent any premium over PRICE2.
The
equation thus becomes:
CSI + B(0) + CP(O) - Y
+ Y1 = PRICE2
The addition of these two variables enables us treat the trans action constraint as a goal, that is, as a "soft" constraint the exact
attainment of which might become subordinated to the attainment of
other goals. In effect, if PRICE2 is specified to be zero and Y1 and
Y1 are not penalized (i. e., included in the objective function), the final
value of Y1 will correspond to that value of PRICE2 which minimizes
the sum of all deviations from their respective targets. Alternatively,
-141-
if a given PRICE2 is specified, and Y1 ind Y1 are heavily penalized,
their final values (if none is a basic variable) may be interpreted as the
"opportunity cost", shadow price or marginal value of $1 of premium
and of discount over the specified price.
Be definition, only of the y's
may appear at a positive value in the final solution.
Then according to
the marginal value concept, that value represents the amount by which
the objective function would decrease with a $1 change (of premium if
Y1 > 0) or of discount if Y1 > 0) in PRICE2, provided the solution
remains feasible. This value becomes very useful in determining the
impact that a proposed price has on the overall attainment of manage-
ment's goals.
2.
Short-Term EPS Dilution Constraint
This constraint specified that earnings-per-share
of the com-
bined firms at the end of the first year (Year 1) should not be less than
the fraction (1 - STDIL*)of their projected level without the merger for
Company 1. STDIL* is, therefore, the maximum EPS dilution that the
acquirer's
management is willing to consider.
For purposes of simplicity, we include the synergistic benefits
expected to accrue from the consolidation in the estimates E2(t) of
earnings for the acquired firm.
The EPS constraint may be expressed as:
-142(1)
EPS3(1) > EPS1(1) * (1 - STDIL )
This inequality can be written in terms of the package variables
as:
E1(1) + E2(1) - ATBIR * B(O) - CPD * CP(O) > El(1) (1-STDIL*)
NOS 1 + CNOS
1
(2)
P1
To the extent that ATBIR * B(O) + CPD * CP(O) represents the fixed
charges generated by any issue of bonds and convertible preferred at
the end of Year 1, we may convert the inequality into an equality by
introducing slack variable Y2 , to represent the amount by which fixed
charges fall short, if at all, from the amount FC* necessary to produce
the maximum EPS dilution allowable (STDIL ), and surplus variable
+
Y2, to represent the amount by which fixed charged may exceed FC
*
We may then write:
E1(1)+E2(1)-ATBIR * B(O)-CPD * CP(D)-Y22 + Y2
2
NOS
+ CSI
P1
and rearranging terms:
E (1) (1-STDIL
-STDIL
NOS 1
(3)
-143-
1 - STDIL
* CSI + ATBIR * B(O) + CPD * CP(O)
PE1
= El(1) STDIL
+ Y
+ E2(1)
(4)
2 -
As defined, Y2 and Y2 represent respectively the positive and
negative deviations (excess and deficit) of fixed charges from the level
FC which corresponds to an EPS dilution equal to STDIL . The reason
for introducing deviations variables expressed in dollar units rather
than in dilution percentage points stems from the necessity of expressing each goal as a linear equation of CSI, B(O), CP(O) and the pertinent
deviations. The inclusion of deviation variables expressed in EPS dilution points would have, in fact, resulted in quadratic equations which
are not amenable to solving through linear or goal programming.
We
shall see later, however, that by linearizing the goal equation, we
actually non-linearize the objective function. Fortunately though, this
does not constitute a grave problem.
3.
Ownership Goal
This goal limits the amounts of common stock to be issued so
that the acquiring company may conserve at least an immediate percentage ownership (control) equal to MINOWN%of the combined forms. We
may express this as:
-144V1
MINOWN
V 1 + CSI
100
or in terms of voting stock shares,
MINOWN
NOS 1
NOS 1 + CSI
100
P1
CSI
Y
+ y
= NOS 1(100-MINOWN*)
P1
4.
MINOWN
Solvency Goal
The goal here consists of maintaining a debt-to-equity ratio
equal to DER . Mathematically, we may express this as:
Di(0) + D2(0) + B(O)
EQ1(0) + CSI + CP(0)
= DER*
(4. 1)
Again, we introduce surplus and slack variables Y4 and Y4 to
denote respectively the excess and shortage of debt over the level D
which, if issued, would produce in conjunction with the issued equity
CSI the target debt-to-equity ratio DER . After rearrangement of
terms, the constraint may be written as:
-145DER
* CSI-B(O)+DER *CP(0) + Y4 - Y = Dl(O)+D2(0)-DER EQ1(1)
5.
Earnings-Per-Share
Growth Goal
This goal consists of making a target amount of EPS by Year N.
That is,
EPS3(N)
> EPS 3
(5. 1)
We may express EPS3 for any year end t as:
El(t) + E2(t) - ATBIR* B(t) - CPD * CP(t)
EPS 3(t)
(5. 2)
NOS1 + CS, + CPCR * [CP(O) - C(t)]
P1
If the bond issue has a sinking fund provision attached to it, requiring annual payments equaling a fraction SFR of the amount issued
B(O), starting on Year t , we may then express B(t) as:
B(0)
for t < t
B(O) [ 1 - (t - t 1 + 1) SFR]
for t > t
p
B(t)
or alternatively as:
-p
- 146 -
B(t) = a * B(O)
where
Iu
for t < t
1
(1 - (t - t 1 + 1) SFR)
P
for t > t
- p
Also, if we estimate the convertible preferred shares to
convert
into common stock according to a schedule, where each
year a given fraction t of the initial issue CP(O) get converted, we
may then express the oustanding amount at each year-end as:
t
CP(t)
= (1
-
)i
i=
* CP(O)
1
The expression inside brackets represents at any year-end t
the non-converted fraction of the issue.
Let us replace it by yt to
obtain:
CP(t) = t * CP(O)
With the expressions for B(t) and CP(t) thus expressable in terms of
their respective initial issue amounts, we may write:
-147-
El(t) + E2(t) - ATBIR *a * B(O) - CPD * yt * CP(O)
EPS3(t)
=
NOS1 + CS, + CPCR * CP(O) * (1 - Yt)
P1
Introducing surplus and slack variables Y5 and Y -to
5
5
denote,
respectively, the amounts by which earnings exceed or fall short of
their target, we now have
E1(N) + E2(N) - ATBIR *a * B(O) - CPD * Yt* CP(O) - Y5+Y5
EPS3
=
NOS + CS, + CPCR * CP(O) * (1 - yt)
P1
or rearranging terms
EPS3*
P1
* CSI + ATBIR *a*
B(O) + (CPD * yt + EPS3
* CPCR) * (1 - t) * CP(O)+ Y5
= El(N) + E2(N) - EPS3
- Y5
* NOS1
Any penalty which may be attached to the underattainment of the
targeted EPS may be discounted into the present and then applied to Y5.
-148-
6.
Net Working Capital Goal
This goal consists in maintaining by the end of the first year the
level of networking capital above a minimum WC . That is,
WC3(1)
> WC
Taking the projected figures for working capital for companies 1
and 2, we must substract from WC1(1) the dividends which shall be paid
on the issued shares and add the dividends which were projected to be
paid by Company 2 to its shareholders,
and which now shall be paid to
the parent company.
WC 1(1) - DIV* CSI
P1
- ATBIR * a * B(O)- CPD * CP(O)
+ WC2(1) + E2(1) * PAY02 > WC
Introducing surplus and slack variables Y6 and Y to represent
respectively the excess and shortage over target of working capital we
may express the goal as:
-149-
DIV * CSI + ATBIR* a * B(O)+ CPD * CP(O)
P1
+ Y
-
Y
= WC(1) + WC2(1) + E2(1) * PAY02-WC
So far, we have examined the various goals to be considered
when structuring the merger package, and have expressed each goal
as a linear equation of the package and corresponding deviation variables.
Let us now consider the objective function to be minimized.
7.
Objective Function
As previously stated the objective of goal programming is to
determine the solution(s) which minimizes the penalty-weighted sum
of the deviations which may re suit.
MIN Z
=
(Pi
*di
+ pi *d
where Piv Pi denote respectively the penalities attached by management
to a positive and a negative deviation from target i;and d
and d
represent respectively the positive and negative deviation which may
result from target i.
d1i = f(Yi1)
-150-
During the formulation of the goal equations, we saw that in
most instances the deviations d. had to be expressed in terms other
than those in which the manager specifies his target.
This transfor-
mation, i. e., di = f(Yi) , while allowing us to express each goal as
a linear equation, constitutes merely a trade-off, for it is done at the
expense of producing a quadratic objective function of the deviation
variables.
Before examining what new complexities are introduced by
this, and how they may be dealt with, let us explain why the objective
function becomes non-linear. For that purpose, let us refer to the EPS
dilution equation:
EPS3(1) > EPS1(1) * (1 - STDIL*)
We converted this inequality into a linear equation by introducing
surplus and slack variables Y2 and Y which represent respectively the
amounts by which the fixed charges resulting from any issues of bonds
or convertible preferred exceed or fall short of the level FC* which
produces an EPS dilution of STDIL . The manager, however, does not
penalize these amounts but rather the percentage points of EPS deviation from his target.
This means then, that we have to determine the
amount of fixed charges which corresponds to one percentage point of
EPS dilution and then attach to it the same penalty as that which the
manager attributes per point of dilution deviation.
version requirement that produces the problem.
It is this basic con-
-15 1-
Recall that the relationship between EPS dilution and fixed charges
for Year 1 may be expressed as:
STDIL(1) = 1 - PEl * I
E l( l )
+ E2(1) - FC(1)
I * (V + PRICE2) - FC(1)
where I stands for the after-tax-bond-interest
rate ATBIR, and the con-
vertible preferred dividend yield CPD, here assumed for simplicity to
be equal.
As can be readily appreciated, this equation has the functional
form of
y =l-ab
which means that there exists a non-linear relationship between dilution
percentage point and $1 of fixed charges.
In non mathematical terms,
this is equivalent to saying that to each EPS dilution point, there corresponds a different amount of fixed charges.
Therefore, if each per-
centage point of dilution deviation is penalized equally, the corresponding
penalty per $1 of fixed charges will be unequal and will depend on the
amount of fixed charged involved. This, in fact, means that the penalty
function, or in other words, the objective function, varies non-linearly
with the amount of fixed charges.
for most of the other goals.
This situation can be shown to hold
-152-
The presence of a quadratic objective function, instead of a linear one, can be generally considered as a drawback, inasmuch as it
adds a dimension of complexity to the problem and to any solution technique. In our case, however, the objective function enjoys the property
of being separable, that is, of being expressable as the sum of n functions, one for each deviation variable Z.:
n
c(Z)
=
C i (Zi)
i=l
and, therefore, enables us to turn to a technique which linearly approximates the original problem and which is amenable to solving by
a version of the simplex method. To keep the exposition simple, we
shall describe the technique for only one variable Z and its associated
function c(Z).
Based upon the knowledge that a surplus or a slack variable Z
may vary between 0 and an upper-bound Z, the technique requires that
a grid of values for Z,
designated
0 = Z 1 < Z 2 <Z
<...
as:
< Z1 = Z
be selected, so that any value of Z may be expressed as a weighted
average of the grid values:
-153Z = W1 Z
+W 2 Z2 +..
+W 1
Z 1
where the weights w must satisfy
Wk = 1
and
Wk > O for k = 1, 2, ...
p
k= 1
In selecting the grid, it is practical to locate no more than two
grid points in any interval of values for Z, where the non-linear function
c(Z) behaves in a linear fashion.
To construct the "approximate" mode, Z must be replaced by
its new expressed in the goal equation; the restriction on the weights
Wk needs to be included as a new constraint; and the non-linear function
c(z) in the objective function must be substituted by the piecewise-linear
or polygonal, approximation:
c Wk Zk
k=l
To illustrate the construction, consider again the EPS dilution
goal equation in its functional form:
y = 1-a
b x
c -x
-154Let p be the penalty per percentage point of positive deviation
from target y
dec
dy
Then letting c denote the total penalty, we have that
p
Since
dy
a c-b
dx
(c - x)
Then
dc
dx
= pa
c -b
(c - x)
2
and the total penalty due to a deviation x - x* is
x
ds
C = pa (c - b)
x*
= pa (c - b)
(c - s)2
1
1
c - x
= pa
c - X*
* x-x*
(c(c- b)
c -x
x*)
-
(c - x*)
-
- 155-
Be definition Z
c(Z + )
= x - x* > 0. Replacing,
= pa
Z+
x* - Z
, (b - x)
(C - X*)
This function has the following graph for Z +
< X*.
c(Z +)
Z2
Z3
Figure 7-1
Z
-156-
Having selected the grid of values Z 1, Z 2 , Z 3 and Z 4 , we may
write any Z+ as:
z + = W11 z
1
+ W2 Z
+ W 3 z 33 + W4 Z
Z22
The objective function,becomes:
)
C(W
= pa
(b - c)
O
W1+ +
(c - x*)
+
z4
z2
+
x* - Z
2
z3
X* - Z 2
+
w3
+
w4
4
x* - Z4
and the corresponding goal equation becomes:
1 - STDIL
PE1
* CSI + ATBIR
+
2
2
* B(O) + CPD
+
+
3
2 + W4
*
CP(O)+ W1 z
4
= E (1) * STDIL* + E2(1)
These equations are now linear functions of CSI, B(O), CP(O),
+
+ w
W1 , W2 ,
W and Y2
-157-
We have illustrated how the quadratic expression of any penalty
function can be linearized by substituting it by a piecewise-linear
proximation.
ap-
Under this new form, the problem can be solved as a
linear programming one. However, in order for us to do so with our
problem, we first have to linearize the penalty functions of all the deviations which may be penalized.
Let us make a rough estimate of what
impact this may have on the problem.
Basing ourselves upon the know-
ledge that linearization is required in the case of three goals, and hence
for six penalty functions (each goal has a surplus and slack variable)
and furthermore, assuming that three grid values will be required to
piecewise linearize each penalty function, it is possible to estimate that
at least eighteen new variables (24 new ones minus the six being linearized) and six new constraints will be added to the probme.
The inclusion of these many additional variables and constraints
not only adds complexity to the envisioned solution technique, but also
increases the time, and thus the cost, needed to arrive at a solution. In
order to avoid this, we have tried to determine (i) to what extent the
penalty functions behave nonlinearly in their respective intervals, and
(ii) what assumptions must be made so that each function may be sub-
stituted by a one-segment, or at most, by a two-segment linear approximation. In what follows, we proceed to determine this for each of the
three nonlinear penalty functions.
-158-
C.
1.
Linearization of Penalty Functions
EPS Dilution Penalty Function
We have already seen in previous illustrations how the short-
term EPS dilution which may result from issuing a given package can
be expressed as a function of the fixed charged that the package may
engender.
y =
_a (b
x)
where
y = short-term
dilution
x = fixed charged
a = PE1 * I
b = El(1) + E2(1)
c = I(V1 + PRICE2)
I = after-tax-bond interest-rate
= convertible referred divident
yield
The graph of the function for Q < x < I * PRICE2 looks like
for different I's:
-159-
_
AL
l~x
0
-5/
-15%
Figure 7-2
In order to determine whether y lends itself to a linear approximation within the pertinent interval of x, we need to examine the varia-
tion of the first -order derivative within the interval, or alternatively,
check whether the absolute value of the second-order derivative remains
throughout the interval smaller than a very small number
. Mathe-
-160-
matically, we express this as:
dy
dx
- a (b - c)
constant
for 0 < x <I * PRICE2
(c - x)
or whether
d2y
2a (b - c)
dx2
(c -x)3
for 0 <x <I * PRICE2
Testing for the last condition, we may replace each parameter by its
corresponding expression to obtain:
E1(1) + E2(1)
PE1
I
- (VI + PRICE2)
I
(V1 + PRICE2) 3 * 1 -
3
X
<
2
I(V1 + PRICE2)
The left-hand side of this inequality will tend to be small if (i)Iis close
to the rate whichthe market is capitalizing the purchaser's earnings:
(ii) if the buying company's value is much higher than the seller's price;
(iii) if the amount of debt (bonds and convertible preferred) issued con-
stitutes a small fraction of the total package.
Assuming that at least one of these conditions holds, we may
linearize y by approximating it by a single linear segment passing by
the point (x, y ) and having a slope equal to the value of the first-order
-16 1-
derivative evaluated at x . The equation of such a linear segment is:
(y
y*) = - a (b - c) (x - x*)
for 0 <x < I * PRICE2
(c -x)2
By definition
Y+
2
= x -x
when x < x < I* PRICE2
= x -x
when O < x < x
and
"
Therefore, after replacing each parameter by its expression, we may
write
-P1 * NOS1
, 1
%2
+
_
21 -
* I - (1. -STDIL*)] 2
E1(1)
P1i NOS1* I[I (V1+ PRICE2)- El(1) - E2(1l
22
and
P1 * NOS1
C 2 (Y2 ) =
* - (1. - STDIL* 2
iEl(l)N
P1 * NOS1
* I[I (V1 + PRICE2) - E(1) El(1)
E2 (1
The penalty Z(Y2 ) due to a positive derivation from x is:
2
-162P2
Z(Y+)
2
100
* C2222
(Y2)
where P2 is the penalty management associated with each percentage
point of excess short-term EPS dilution.
Correspondingly, the penalty given a deficitary amount of fixed
charges, if at all penalized, is:
_
P22
Z(Y2 )
where P2
100
-
*, C2 (Y2 )
= the specified penalty per percentage point of underattainment.
2.
Ownership Penalty Function
Proceeding again along the same lines, we express the result-
ing ownership percentage as a function of the amount ISH of shares
issued:
OWN
=
NOS 1
NOS+ CSI/P1
NOS 1
NOS 1 + ISH
The first and second-order derivatives are:
-163d OWN
- NOS 1
d SH
(NOS 1 + ISH)2
d 2 OWN
d
ISH2
< 0
NOS1
(NOS 1 +
ISH)3
>0
The graph of the function looks like:
Owners)ip
OWN
400o
OWN"
ISH
ISH*
PRICEZ
P1
Figure 7-3
(continued on page 167)
PAGES (S) MISSING FROM ORIGINAL
PAGES (S) MISSING FROM ORIGINAL
PAGES (S) MISSING FROM ORIGINAL
-167-
It is clear both the expressions for the first- and second-order
derivatives that we may approximate the OWN curve by a linear segment
if (i) the buying company's number of outstanding shares NOS 1 is great
and/ or if (ii) the number ISH of issued shares is small in relation to
NOS 1.
Assuming that these circumstances hold, the equation for the
linearizing segment can be expressed:
NOS
(OWN - OWN ) = (NOS1+ISH*)
2
(NOS
1 +ISH
*
(ISH - ISH )
)
The corresponding penalty costs for a positive and negative deviation
*
from OWN are
+
z(y3)
P3
100
+
z(y 3 )
OWN
N
P3
100
*
P3
* C(Y 3)
100
P3
100
NOS
NOS
*
* C(Y+)
(NOS1 + ISH*)2
100
+
3
O2
Y+
3
1
P3
*
OWN
NOS 1
*
NOS 1
2
(NOS1 + ISH*)
100
*2
*
*
Y3
* Y3
-168-
3.
Solvency Penalty Function
Expressing the debt-to-equity ratio as a function of the amount
X of debt which may be issued yields:
DER
=
D1(0) + D2(0) + X
EQ(1) + (PRICE2 - X)
The first- and second-order derivatives of this function are:
d DER
dX
d2
DER
d
X2
D1(0) + D2(0) + EQ1(0) + PRICE2
(EQ1(0) + PRICE2 - x)
2 (D 1(0) + D2(0) + EQ1(0) + PRICE2)
(EQ1(0) + PRICE2 -
X)3
> 0
> 0
The graph of the pertinent curve looks like:
DER
DE R*
Figure 7-4
IKILtX,
-169-
Inspection of the expression for the second-order derivatives
reveals that within the 0
x < PRICE2 interval, the curve may be
approximated by a linear segment only (i) if the buying company is
much larger than the selling one and (ii) if both the purchasing and
selling companies possess nearly non-leveraged financial structures.
For those few cases where both of these conditions hold, the equation
for the pertinent linear segment can be written as:
(DER
- D1(0)
DER+ D2(0)+ EQ(0) + PRICE2 (X X*)
(EQ 1(0) + PRICE2 - X )
For those other cases, where the second condition does not hold, we
have resorted to piecewise linearizing the penalty function by two seg-
ments, as illustrated below:
rnf
YfILItZ
-
15,
I
V
X
-170-
By linearizing DER in this simple manner, we avoid introducing
new variables and constraints to the problem.
The equation for a posi-
tive deviation from DER becomes:
1 + DER
DER - DER
* (X - X)
forX < X < PRICE2
EQ 1(0)
and replacing X - X by Y 4 ,
1 + DER
= DER - DER
C 4 (Y+)
4
Z
EQ 1(1)
*Y4
The penalty to any amount Y4 is then
+
P4
100
* C(Y4)
4
P4
100
1 + DER
* Y4
EQ 1(1)
where p denotes the penalty attached per percentage point of excess
debt-to-equity ratio.
Correspondingly, the equation for a negative derivation from
DER
is:
DER - DER
1 + DER
(EQ1(1) + PRICE2)
and replacing X - X by Y
we have
* (X - X ) forO <X <X
- 17 1-
+
C(Y 4 ) = DER - DER
1 +DER
=
J'
EQ 1(1) + PRICE2
Y +4
The penalty due to any shortage of debt issued is
P4
Z(y 4 )
1 + DER
fi
EQ1(1) + PRICE2
100
Y4
where p4 represents the penalty attached to each percentage point be-
low the target debt-to-equity ratio DER .
Having substituted each nonlinear penalty function by a piecewise linear approximation, we may finally express the objective function
+
as a linear equation of the positive and negative deviations from each
goal:
6
+
Min Z o =
+i-
[Pi * Ci(Y)+Pi
i=1
* Ci(Yi
where
C (Y+ )
C 1(Y
C (Y)
2
2
)
+
Y1
=Y 1
E1()
1*I - (.
-STDIL
)l2
P1 * NOS * II (V1 + PRICE2) - E1(1) - E2(1
El(l)
* Y2
-172-
P1 * NOS1 * I - (1. - STDIL' ) 2
E1(1)
C 2 (Y2 )
PEl(1*N
*I
(V1 + PRICE2) - El(l) - E2(1)
.,l~l
= ((OWN )2/100*NOS 1)* Y3
C3(Y)
C 3 (Y 3 ) = ((OWN*)2/100*NOS1Y
Y3
= (100 * (1 +DER)/EQ1(1))
C44 (Y)4
C4 (Y4 ) = (100 * (1 +DER)/(EQ1(1)
C(Y4)
+
c 55 (Y5)
= Y55
5
C 5 (Y5 )
C66 (Y)6
C 6 (Y
6
=
=Y
)
=
y
5
6
6
Y44
+ PRICE2))
Y4
-173CHAPTER VIII
The Use of Computers in Merger Analysis
A.
Introduction
The purpose of this chapter is to examine the potential uses of
computers in financial acquisition analysis. Thus far, we have presented several methods for acquisition valuation purposes, and have
proposed a normative framework for such kind of analysis. In this
chapter, we intend to examine to what extent computers can and/or
are being used in merger analysis as an aid to decision-making.
We begin by briefly reviewing some of the characteristics
of
merger analysis which make computers especially appropriate tools
at all stages of the analysis.
The discussion continues with an evalua-
tion of the pros and cons that the use of computers may present.
After examining the major characteristics and differences of
the available programs, each program is described in terms of its
purpose, scope and input/output features and requirements.
A brief
critique follows each such description.
Lastly, we discuss howthe several programs may be used
within the analytical framework proposed in Chapter VI. We conclude
the chapter with a concise comparison of the programs described.
- 174The sources of information which were tapped to obtain the
material herein presented consist mainly of articles having appeared
in financial and accounting journals from 1967 to date. Most articles
focus primarily on the potential applications of the programs, and do
not contain information related to program costs, programming languages, program sizes, etc.
Our presentation is limited to what information we found available.
1.
Characteristics of Merger Analysis
The use of computers as an aid to executive decision-making
has led to significant improvements in the quality, breadth and depth
of merger analysis, especially in the financial area. These improve ments, moreover, have been accompanied by equally significant cost
reductions.
Typically, the analysis of an acquisition or a merger candidate
consumes large quantities of a company's high level line, staff and
consulting professionals' time. This stems from the inherent characteristics of and circumstances under which the analysis is usually
performed:
i.
A great need for secrecy, particularly since the stock
price of the buyer might be affected one way or another by
- 175-
speculative trading either in contemplation of possible merger
or even by rumored or actual discontinuance of interest or consideration.
ii.
Ever-changing input data.
iii.
Consideration of a great number of financial and non-
financial topics.
iv.
Considerable uncertainty as to the impact of the merger
on future financial results.
v.
The need to examine a wide variety of possible alterna-
tive exchange packages.
vi.
A considerable amount of computation.
To these characteristics, it is necessary to add the fact that the
acquisition study group typically consists of only a few people. This
manpower constraint limits the amount of time available for analysis
and as a result, the financial aspects of the acquisition are often not
given the same depth of scrutiny as the other areas of merger analysis,
such as market potential, organization, product-fit, and personnel
requirements.
2.
Advantages and Disadvantages of Computer Analysis
The computer's advantages in acquisition analysis include the
following:
-176-
i.
The analysis is performed consistently and quickly.
ii.
A considerable amount of executive time is freed
for use in other key analysis areas.
iii.
Greater secrecy, even if the actual operations of the
computer are not performed by personnel in management's
confidence (e. g., computer staff and operators).
iv.
A greater variety of assumptions and payment alterna-
tives may be considered.
The potential disadvantages to computer analysis stem from the
attitude of the people involved, rather than from the computer itself.
These may be:
i.
The placement of undue weight on the numbers when
making decisions.
ii.
The analysis may bog down because too many alternatives
are considered and the analyst and decision-maker become inundated with printouts or because they become so intrigued with
examining alternatives they forget that a decision has to be made.
iii.
Problems can arise in shifting from manual to computer
analysis, especially if the merger analysts do not write the programs.
- 177-
iv.
Computer programs fix the mode of analysis and the key
variables to use. The analysis framework adopted in a program
may not fit the user's requirements.
3.
Characteristics
and Differences of Available Programs
A number of standard programs are available for computer analysis which can be used by most companies in their present form or
with slight modifications.
Because of the large number of calculations
required in acquisition analysis, most programs adopt a simulation
approach to forecast the future operations and financial results of a
company.
The first and major difference between the various merger programs in existence is their purpose and scope. Some programs serve
to perform preliminary investigations of a wide range of issues, while
others perform detailed investigations of only a few issues. There are
only a few programs which may be used to analyze a wide number of
considerations in depth.
A second major difference between the programs concerns the
amount and type of information required before they can be used. Some
programs require estimates about the future; others require past data
and obtain their projections by extrapolating past trends.
A third principal difference relates to the mode in which the
programs are designed to be run. Some are programmed to be run in
-178-
a batch processing environment, whilst others are designed for interactive usage. We shall provide comments on this technique as part of
the description of the FUSION program. (Chapter IX, Section 1)
The fourth difference between the programs relates to the
amount,detail and flexibility of their respective outputs. Clearly, more
detailed results are required from in-depth analyses than from preliminary investigations. Also, more flexibility in the choice of possible
output formats is required from interactive programs than from batchmode ones.
A fifth difference between programs concerns their ability to
take uncertainty into consideration when performing the analysis.
Most of the programs in existence make their calculations in a deterministic fashion, i. e., the values entered into the program as assumed
to have no uncertainty associated with them.
Hence, in order for an
analyst to get a feeling of the range of possible values that a variable
may assume in the future, he must run the program over and over
again, using different combinations of input values every time.
- 179-
B.
The Available Programs
The description of the programs which we were able to review
will be given in terms of the purpose, scope, logic, types of output and
amount of information required by each. We shall start with the pro-
grams which are available for batch-processing applications, and then
describe those which are meant to be run in an interactive mode. A
short critique will follow each description.
In those cases where the
programs were not named, we have referred to them by the name of
their author(s).
In all cases, our presentation is based upon the des -
cription provided by the authors.
We refer the reader to the pertinent
articles for more details.
1.
The McKinsey Program
The McKinsey Program is a computer model developed during
1968 and 1969 which "combines long-range planning with individual
candidate analysis". It enables a potential acquirer to asses its actual
needs for acquisition in the context of its overall corporate objectives
and alternative growth opportunities.
The model requires the chief executive officer to examine the
company's long-range growth goals and decide if they can be met by
internal growth before he considers following the acquisition route. If
he decides he must look outside to achieve his goals, the model allows
1Richard W. Kraber, "Acquisition Analysis: New Help from
your Computer", Financial Executive, March 1970.
-180-
him to test the compatibility of a possible acquisition, viewed both
in terms of its impact on parent and candidate stockholders and on
the corporation's capital structure and future acquisition plans.
In order to use the McKinsey Program, a company needs to
follow the following five steps:
Develop a Corporate Growth Plan
Step 1:
In order to determine whether internal growth alone fulfills
the corporate objectives, the company must collect current data and
develop a range of projections for its performance for the next five
to ten years.
The pertinent data to use for this purpose is presented
in the left-most column of Exhibit 1, where for simplicity, single
point estimates have been used. In a real case, a range of projections
may be developed for each year.
Using these numbers as input data, the computer model simulates the operations of the firm and develops a six-year picture of the
firm's income statement, balance sheet and funds flow statement (see
Exhibit 2). The output figures can then be analyzed and compared
against the firm's corporate financial objectives and policies.
If in-
ternal growth alone does not suffice to meet the company's long-range
goals, the firm must takethe next step and move towards an integrated
acquisition program.
-181-
EXHIBIT
1
CURRENT AND
PROJECTED FINANCIAL
Superior
Tree
DATA
Typical
Home Building
Company
Deluxe
Homes
Status at end of 1968
Sales (millions)
Common shares outstanding
Common dividend per share
Common stock price
$100
1,000,000
$1.92
$84
20
$4.20
Price/earnings ratio
Earnings per share
Working capital (millions)
$20
Fixed assets (millions)
Debt (millions)
Debenture (millions)
Preferred stock (millions)
Common stock and
$80
$20
$5*
$35
1,000,000
1,000,000
$1.16
$1.CO
$53
20
$40
20
$2.65
$2.00
$8
$7
$28
$18
$16
$17
$24
$5**
retained earnings (millions)
Projected Performance
$30
$70
1969-1974
Sales annual compounding growth rate
10%
17%
18%
10%
20%
7%
50%
20
15%
7%
50%
20
.2
Profit before interest and tax as a
percent of sales
Average interest on debt
Average tax rate
Price/earnings ratio
Working capital-to-sales ratio
7%
50%
20
.2
Declining to
.6 by 1974
Fixed assets-to-sales ratio
.8
.8
Dividend payout as a percent of
EPSafter preferred dividends
50%
40%
40%
$5 million
None
Issuance of Common Stock
None
in
1969 and $10
million in 1972
*50,000 debenture shares convertible into 100,000 shares of common; interest per debenture share
is $5; issue callable in 1971 at $160 per share.
**50,000 preferred shares convertible into 100,000 shares of common; dividend per preferred share
is $4; issue callable in 1970 at $170 per share.
Table 8-1
- 182 -
_ __
__ _ _I _-
EXHIBIT 2
FINANCIAL
TREE BEFORE ACQUISITIONS
PICTURE OF SUPERIOR
1969
INCOME STATEMENT
110.00
SALES
11.00
PROFIT BEF INT + TAX
1.89
INT ON DEBT + DEBNTUR
4.56
PROFIT AFT INT + TAX
0.
OTHER AFTER TAX INCOME
0.20
PREFERRED DIVIDENDS
NUMB OF COM SH OUTSTNG 1.00
4.36
EPS AFTER PFD DIV
2.18
COM DIV/SHARE
0.20
COM SH OVERHANG
EPS AFT PFD + DEB CONV
3.90
87.10
COM STOCK PRICE
FUNDS FLOW
2.18
RETAINED EARNINGS
0.
PLUS COM STK ISS/REPUR
2.00
LESS INCR IN WRKNG CAP
3.60
LESS INCR IN FIXED AST
-3.42
NET FUNDS FLOW
BALANCE SHEET
22.00
WORKING CAPITAL
83.60
FIXED ASSETS
23.42
DEBT
5.00
DEBENTURES
5.00
PREFERREDSTOCK
72.18
COM STK + RET EARN
SUPERIOR DEBENTURE ISSUE #1
SUPERIOR PREFERRED ISSUE #1
1972
1973
1974
146.41
14.64
161.05
177.16
17.72
1970
1971
121.00
133.10
12.10
13.31
2.12
4.99
2.08
5.62
2.27
6.19
2.44
6.83
3.09
7.32
0.
0.
0.
0.
1.20
0.
0.
1.20
0.
0.
1.20
0.
0.
1.20
4.68
2.34
5.16
2.58
5.69
2.85
0.
0.
0.
5.69
1.10
4.54
2.27
0.10
4.26
90.77
2.50
0.
2.20
3.52
-3.22
24.20
87.12
26.65
5.00
0.
79.67
CONVTD IN 1971
CONVTD IN 1970
Table 8-2
4.68
93.62
2.81
0.
2.42
3.39
16.11
6.10
113.88
6.10
121.92
3.09
3.42
3.66
0.
0.
2.93
2.93
0.
5.16
103.10
2.66
3.19
6% year
3.05
0.
3.22
9.66
-3.00
-2.76
-2.44
-9.23
26.62
90.51
29.28
32.21
93.70
29.65
32.41
0.
0.
96.63
34.85
35.43
106.29
44.08 31%
0.
0.
87.48
90.58
0.
0.
93.99
0.
0.
97.65 69%
-183-
Step 2:
Develop an Acquisition Growth Strategy
The acquisition staff returns to the computer and determines
whether a hypothetical multi-acquisition program can help the firm
achieve its objectives. This requires that the financial characteristics of a typical company operating in the industry grouping that the
firm wishes to enter be determined. These figures are then entered
into the computer, which performs several test-runs using different
combinations of acquisitions and assuming different timings for the
acquisitions (see Exhibit 3).
If no feasible program results in the attainment of corporate
objectives, the firm must decide whether to supplement the acquisition
program with diversification into other industries or to revise corporate
objectives.
Step 3:
Screen the Many to Find a Few
With an acquisition program that integrates diversification
ambitions with the firm's internal growth, the staff must now seek out
the most attractive acquisition candidate.
Using published data, the staff must develop forecasts for profit growth by providing forecasts for the next six years for each of its
basic components: sales, profit margin, interest cost, tax rate, etc.
The information is then fed into the program which produces a
six-year income statement, balance sheet, and funds flow for the candidate (see Exhibit 4).
EXHIBIT
-1A-
EXHIBIT 3
ACQUIRING
A TYPICAL
HOMEBUILDING
SUPERIOR
IN 1969, 1970, AND 1971
COMPANY
1969 1970 1971 1972 1973 1974
INCOME
STATEMENT
145.10 203.13 277.25 315.06358.37 408.02
SALES
PROFIT
BEFINT+ TAX
18.02 28.53 42.14 48.37 55.57 63.89
INTONDEBT
+ DEBNTUR 3.56
6.03
8.90
9.95 11.13 12.95
DEPR
OFWRITTEN-UP
AST 0.17
0.37
0.64
0.71 0.71
0.71
PROFIT
AFTINT+ TAX
7.15 11.06 16.30 18.85 21.86 25.11
OTHER
AFTER
TAXINCOME 0.
O.
0.
O.
0.
0.
AMORTIZATION0.17
GOODWILL
0.64
0.37
0.71 0.71
0.71
PREFERRED
DIVIDENDS 0.20
0.
0.
0.
0.
0.
SHOUTSTNG1.63
NUMB
OFCOM
2.45
3.35
3.35
3.35 3.35
EPSAFTER
PFDDIV
4.16
4.36
4.67
5.41
6.31
7.28 10%year
2.08
COMDIV/SHARE
2.33
3.64
2.18
2.70
3.15
COMSHOVERHANG
0.20
0.
0.10
O.
O.
0.
EPS
AFTPFD+ DEBCONV 3.88
4.24
4.67
5.41
7.28
6.31
COMSTOCK
PRICE
87.28 91.53 98.02 119.00 138.76 160.06
FUNDS
FLOW
RETAINED
EARNINGS
3.39
5.35
7.83
9.07 10.57 12.20
COMSTKISS/REPUR 0.
PLUS
0.
0.
0.
0.
0.
PLUS
WRTN-UP
ASTDEPR 0.17
0.64
0.37
0.71
0.71 0.71
PLUSGOODWILL
AMORTIZ 0.17
0.64
0.71
0.37
0.71 0.71
LESSINCR
IN WRKNG
CAP 2.00
2.42
2.20
2.66
2.93 3.22
LESS
INCRIN FIXED
AST
7.63 13.07 20.14 22.80 25.86 36.50
NETFUNDS
FLOW
-5.96 -9.18 -13.45 -14.96 -16.79 -26.09
BALANCE
SHEET
WORKING
CAPITAL
22.00 24.20 26.62 29.28 32.21 35.43
FIXED
ASSETS
111.68 152.83 205.82 228.62 254.49 290.99
WRITTEN-UP
ASSETS
4.86 10.58 17.08 16.36 15.65 14.94
GOODWILL
4.86 10.58 17.08 16.36 15.65 14.94
DEBT
47.21 82.34 126.85 141.82 158.61 164.7052%
0.
O.
DEBENTURES
5.00
O.
0.
5.00
0.
0.
PREFERRED
STOCK
5.00
0.
0.
0.
COMSTK+ RETEARN 126.39 199.80 285.83 294.90 305.47 317.6748%
SURPLS
FROM
ACQ
-40.20 -88.95 -146.08 -146.08 -146.08 -146.08
ISSUE
#1 CONVTD
IN 1971
SUPERIOR
DEBENTURE
SUPERIOR
PREFERRED
ISSUE
#1 CONVTD
IN 1970
EXHIBIT 4
Table 8-3
FORDELUXE
HOMES
FINANCIAL
PROJECTIONS
1969 1970 1971 1972 1973 1974
INCOME
STATEMENT
41.30 48.73 57.51 67.86 80.07 94.48
SALES
6.20
7.31
8.63 10.18 12.01 14.17
PROFIT
BEFINT+ TAX
1.66
2.14
1.99
2.65
3.43
INTONDEBT
+ DEBNTUR 1.25
2.47
2.83
3.24
4.09
4.68
5.37.18%
PROFIT
AFTINT+ TAX
0.
0.
0.
0.
0.
OTHER
AFTER
TAXINCOME 0.
0.
0.
0.
0.
0.
PREFERRED
DIVIDENDS 0.
1.30
1.30
1.12
1.12
1.30
NUMB
OFCOM
SHOUTSTNG1.12
2.20
2.51
2.88
3.15
3.61
4.14
EPS
AFTER
PFDDIV
1.00
1.00
1.15
1.26
1.44
1.65
COM)IV/SHARE
0.
0.
0.
0.
0.
0.
COMSHOVERHANG
2.51
2.88
3.15
3.61
4.14
EPS
AFTPFD
+ DEBCONV 2.20
43.98 50.24 57.69 63.08 72.12 82.74
COMSTOCK
PRICE
FUNDS
FLOW
3.22
2.46
2.81
1.95
1.35
1.70
RETAINED
EARNINGS
0.
0.
10.00
0.
0.
PLUS
COMSTKISS/REPUR 5.00
2.44 2.88
2.07
1.75
1.49
LESS
INCRINWRKNG
CAP 1.26
9.77 11.53
8.28
7.02
5.04
5.95
LESS
INCRIN FIXED
AST
2.11 -9.41 -11.19
0.05 -5.74 -6.83
NETFUNDS
FLOW
BALANCE
SHEET
9.75 11.50 13.57 16.01 18.90
8.26
WORKING
CAPITAL
33.04 38.99 46.00 54.29 64.06 75.59
FIXED
ASSETS
17.95 23.69 30.51 28.41 37.81 49.00 52%
DEBT
O.
0.
0.
O.
0.
0.
DEBENTURES
O.
O.
0.
0.
0.
0.
PREFERRED
STOCK
23.35 25.04 26.99 39.45 42.26 45.4848%
COM
STK+ RETEARN
Table 8-4
-185-
Step 4:
Analyze Financial Impact of Candidates
This step requires that the exchange terms which will most effectively satisfy the diverse interests of the stockholders and of the
respective acquisition candidates be determined. These terms include
the purchase price and the exchange media-cash, debentures, preferred stock, or common stock.
The analysis is performed by test-running several combinations
of prices and exchange packages, and by generating for each combination a consolidated income statement, balance sheet, and funds flow.
Once a few alternatives have been selected, the model is used
again to produce a new output giving a before-and-after
acquisition
financial picture in terms of (i) EPS after preferred dividends; (ii) DPS
received by a candidate stockholder; and (iii) value of stock held plus
cash received by a candidate common stockholder (see Exhibit 5).
In developing a negotiation strategy, the staff must balance the
change in the firm's EPS in relation to the dividends received and stock
value held by a candidate stockholder.
Finally, before starting negotiations, the staff must calculate
the total financing inpact of the acquisition with one or two exchange
combinations. The analysis places the candidate's capital structure
under close scrutiny, and uses the model to simulate the consolidated
financial performance six years into the future (see Exhibit 6).
-186-
EXHIBIT 5
SUPERIOR
TREE ACQUIRING
DELUXE HOMES
IN
1969
EPSAfter Preferred Dividends on Superior Common Stock
MKT
- PERCENT OFPREM
CASH
PREF
EPS BEFORE LAST ACQ
0.
0.
0.25
0.25
0.
0.50
0.25
0.
0.20
0.35
0.
0.
0.
0.35
0.50
0.20
0.35
0.
1.00
0.50
0.80
1.00
0.50
0.80
1969
4.36
4.16
4.14
4.15
4.04
3.99
4.01
1970
4.54
4.50
4.53
1971
1972
1973
4.68
5.69
6.07
4.51
4.85
4.79
4.87
4.82
5.16
5.40
5.58
5.47
5.38
5.58
5.46
4.46
4.48
4.46
4.82
4.90
1974
6.10
6.71
6.33
7.07
6.19
6.07
6.36
6.20
6.72
7.14
6.87
6.90
Amount of Dividends Received by a Deluxe Common Stockholder
MKT
-PERCENT OFPREM
CASH
PREF
DPS BEFORE ACQUISITION
0.
0.25
0.
0.
0.25
0.50
0.20
0.
0.25
0.
0.
0.35
0.50
0.35
0.
0.20
0.
0.35
COM
1969
1.00
1970
1.00
1.00
1.24
1.34
0.50
0.80
1.87
0.99
1.92
1.07
1.00
1.30
1.43
0.50
0.80
1.99
1.03
2.07
1.15
1971
1.15
1.43
1.98
1.15
1.54
1972
1.26
1.61
1973
1974
1.44
1.65
1.81
2.00
2.08
1.30
0.94
1.05
1.G4
1.73
1.95
2.13
2.25
1.24
1.40
1.02
1.59
1.47
2.16
1.15
1.78
Value of Stock Held Plus Cash Received by a Deluxe Common Stockholder
-PERCENT OFMKT
CASH
PREF
PREM
COM STOCK PRICE BEF ACQ
0.
0.
0.25
0.
0.50
0.25
PLUS CASH OF
0.20
0.
0.25
PLUS CASH OF
0.
0.
0.35
0.35
0.
0.35
PLUS CASH OF
0.20
0.
PLUS CASH OF
0.50
COM
1969
1970
50.24
1.00
0.50
43.98
52.05
50.86
0.
56.21
54.02
0.
0.80
41.48
10.00
45.07
1.00
0.50
54.58
53.91
0.
0.80
43.33
10.80
60.15
57.75
0.
48.16
0.
0.
1971
57.69
60.24
58.43
0.
48.51
0.
64.63
1972
1973
1974
63.08
70.73
72.12
79.53
41.42
37.50
64.87
82.74
87.85
69.73
0.
57.33
0.
62.74
76.14
75.35
0.
52.01
61.76
0.
0.
0.
0.
85.88
44.97
40.50
70.17
0.
Table 8-5
(continued on page 188)
46.30
0.
71.99
0.
95.10
50.49
0.
78.12
0.
PAGES (S) MISSING FROM ORIGINAL
-188-
EXHIBIT 6
SUPERIOR
TREE ACQUIRING
1969
INCOME STATEMENT
SALES
151.30
PROFIT BEF INT + TAX
17.19
INT ON DEBT + DEBNTUR
3.51
DEPR OF WRITTEN-UP AST
0.
PROFIT AFT INT + TAX
6.84
OTHER AFTER TAX INCOME
GOODWILL AMORTIZATION
0.
PREFERREDDIVIDENDS
0.20
NUMB OF COM SH OUTSTNG
1.60
EPS AFTER PFD DIV
4.16
COM DIV/SHARE
2.08
COM SH OVERHANG
0.20
EPS AFT PFD + DEB CONV
3.88
COM STOCK PRICE
87.44
FUNDS FLOW
RETAINED EARNINGS
3.32
PLUS COM STK ISS/REPUR
0.
PLUS WRTN-UP AST DEPR
0.
PLUS GOODWILL AMORTIZ
0.
LESS INCR IN WRKNG CAP
3.26
LESS INCR IN FIXED AST
8.64
NET FUNDS FLOW
-8.58
BALANCE SHEET
WORKING CAPITAL
30.26
FIXED ASSETS
116.64
WRITTEN-UP ASSETS
0.
GOODWILL
0.
DEBT
46.58
DEBENTURES
5.00
PREFERRED STOCK
5.00
COM STK + RET EARN
123.32
SURPLS FROM ACQ
-33.00
SUPERIOR DEBENTURE ISSUE #1
SUPERIOR PREFERRED ISSUE #1
DELUXE HOMES
1970
1971
169.73
19.41
190.61
21.94
4.63
4.16
IN
1969
1972
1973
1974
214.27
24.82
5.43
241.12
28.12
271.64
31.89
7.80
6.31
0.
0.
0.
0.
7.62
8.65
9.70
10.90
0.
0.
0.
0.
0.
0.
0.
0.
0.
1.70
1.80
4.82
0.
0.
0.
1.80
4.50
2.25
2.41
0.
0.10
4.32
94.43
4.82
3.81
0.
0.
0.
6.71
0.
0.
4.85
5.45
6.02
0.
0.
0.
0.
0.
0.
0.
0.
0.
-9.34
-10.25
-11.36
133.61
5.37
6.71
147.60
12.70
6.10
21.19
-12.62
-21.27
38.12
136.51
42.85
147.99
48.22
160.69
54.33
181.88
0.
0.
0.
0.
O.
0.
5.00
0.
132.13
0.
0.
66.18
0.
0.
141.46
0.
0.
146.31
-33.00
-33.00
-33.00
126.11
0.
0.
55.92
CONVTD IN 1971
CONVTD IN 1970
Table 8-6
Table 8-6
77.54
93.15
0.
0.
151.76
-33.00
8%
3.35
4.33
4.73
11.48
6.07
1.80
101.21
9.47
33.95
0.
1.80
6.07
3.04
5.40
118.82
0.
0.
0.
4.17
10.41
3.69
5.40
2.70
0.
12.04
0.
0.
0.
111.43 47%
0.
0.
157.78 53%
-33.00
-189-
Step 5:
Negotiate with Candidate
During negotiations, the acquirer refines his assumptions ab out
the future performance of the candidate and possible sets of exchange
and continually uses the model to update the overall acquisition
terms,
picture.
The McKinsey model is nothing other than an accounting simulation program, which can indeed serve a wide range of uses in any enterprise.
When applied to acquisition analysis, the five steps to be taken
are necessary and relevant if the acquisition candidates are publiclyowned corporations, from which financial data is readily available. For
cases involving non-public acquisition candidates, however, Steps 3 and
4 might not be able to be taken before actually starting the negotiation
process, i. e., Step 5. This fact may have the following consequences:
i.
Additional chances for the acquistion not taking place.
ii.
Additional costs for the whole acquisition program due
to the lower rate of success which is likely to occur.
iii.
Longer negotiations,which may result in
iv.
Increased chances of an information leakage to the public
concerning the possible merger.
These drawbacks', however, are circumstancial and unavoidable
when the acquisition target is a privately-owned firm, of which little is
-190-
publicly known. Therefore, these points do not constitute a weakness
inherent to the program (this point holds for all the other programs
which were designed primarily for public company acquisitions.
Con-
sequently, we shall not repeat this critique in subsequent program
critiques. )
From a financial viewpoint, the major limitation of the program
is posed by the framework adopted for analysis, i. e., an accounting
framework.
The program does not provide the means for performing
discounted cash-flow analysis, probabilistic assessments of future out-
comes or sensitivity analysis on the projected financial results of the
combined entity. Furthermore,
the program can only be run in one
mode, namely, in that where the accounting data is supplied to the program and the program then produces the balance sheet, income and funds
flow statements for the next six years. The inverse process, that is,
where one supplies future objectives and the program determines the
present conditions which must exist in order to attain the objectives,
cannot be implemented.
on a trial-and-error
This means that the program can only be run
basis, fact which in view of the large number of
combinations which may have to be tried out, may result in high com-
puter and staff-time costs. Clearly, though, whatever these costs may
turn out to be, they will not only represent a considerable improvement
over those which would accrue from manual analysis, but will also be
much more justifiable in terms of the quality, quantity and breadth of
their product.
-1912.
The QUICKSCAN Program
2
Developed by John D. Glover, David F. Hawkins and Andrew
McCosh in early 1967, QUICKSCANprovides information on the immediate effects of a merger in which bonds and/or common stock are
to be issued and in which dilution of earnings -per-share
importance to the parent company management.
is of primary
The program was de-
signed to screen a large number of potential acquisition candidates at
an early stage of the acquisition search.
By examining a large num-
ber of premium levels, the program provides the means of determining
the sensitivity of the results to differences in premiums paid for the
acquisition over the current market price f its stock. Through a
built-in two-level screening system, QUICKSCANis useful in performing a preliminary survey of transaction packages which are not feasible
and for the identification of acquisition candidates which are unusually
attractive.
Depending on the version of the program, it may be run in
two modes: one in which the transaction package is predetermined and
the model outputs the resulting financial data, and one in which the maximum immediate short-term dilution is specified and the model determines the package which would produce that dilution. There exist a
version which allows the two modes to be implemented simultaneously
and results to be printed on a same output page. Table II is a printout
of such a version of QUICKSCAN, where for each premium level
2 John
D. Glover, David F. Hawkins and Andrew McCosh, "The
Use of Computers in Merger Analysis, " Mergers and Acquisitions,
Summer 1967.
-192-
considered, three alternative exchange offers have been considered:
(1) the mixes of stock and bonds leading to a zero dilution of earnings
per share; (2) a straight exchange of common stock; and (3) an exchange offer which includes 70 percent stock and 30 percent bonds
(issued at 6 percent).
The information required by QUICKSCANand which was used
to produce Table 8-7,is presented below along which the corresponding
acronyms that we have used throughout our discussions.
Appendix H
includes the listing and sample output pages of our own version of QUICKSCAN.
Information Required from Acquiring Company
Acronym
Item
Number Used
for Example
E 1(0)
Current company dollar earnings estimate,
this year ($M)
$49.4 M
P1
Current stock price, per share
$85.21
DPS(9)
Current dividend per share
$ 2. 10
BIR
Interest rate on bonds to be issued, if any
6%
NOS 1
Number of shares outstanding, now
9.22 M
D(9)
Current debt outstanding
$91 M
Information Required from Candidate Company
E2(0)
Current company dollar earnings (estimated
or actual ($M)
$11.2 M
P2
Current stock price
$58. 75
NOS2
Number of shares outstanding, now
D2(0)
Current debt outstanding
3.56 M
$26. 0
-193-
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- 194-
The QUICKSCAN
program constitutes a useful tool to determine
the immediate impact of an acquisition on earnings -per-share.
How-
ever, granted the fact that immediate EPS results were viewed as the
main criteria of attractiveness for a merger at the time the program
was created, we have already seen that it is by no means the only one
that affects a stock's price.
To this extent, therefore, we find QUICK-
SCAN very limited as a screening tool. Insofar, however, as the current debt levels of the acquiring and candidate firms must be entered
into the program, its scope and validity as a merger screening tool can
be increased at no extra cost by calculating and using the debt-to-equity
ratio as a criteria for candidate selection. In its present form,
QUICKSCANis nothing else than a useful EPS computational tool.
As most of the merger analysis computer programs, QUICKSCAN
assumes that the acquisition candidate is a public firm. This, however,
does not constitute a liability if the purchase concerns a private firm. In
such a case, the acquirer will input into the program the pertinent values
as they are being considered through the course of negotiations.
3.
MERGERESTIMA TOR 3
Developed by the same team which designed QUICKSCAN, MER-
GERESTIMATOR
subjects to more detailed analysis the best acquisition
candidates, as selected by QUICKSCAN.
2Idem.
-195-
In twenty-nine pages of analysis, it provides answers to a high
proportion of the questions management is likely to ask with regard to
the financial aspects of possible acquisition arrangements with each
company examined. The program compares the present with projected
situations in the future by using historic trends (perhaps modified by
management's projected estimated of future developments) to project
financial results five years out on a pro-forma basis. Such projections,
although subject to varying degrees of uncertainty, provide a basis for
analyzing and discussing future possibilities of the acquisition program.
Three basic types of merger-exchange packages are considered
by the MERGERESTIMATORprogram:
(i) common stock only; (ii) com-
mon stock plus bonds, which may or may not include convertible features;
and (iii) common stock plus preferred stock, which may or may not be
convertible.
In the case of convertible bonds and convertible preferred
shares, it is necessary not only to specify the bond interest rate and the
preference dividend rate, but also a conversion price or ratio on each
$100 principal amount of the particular security.
Although the program
is designed so that any conversion rate might be specified by the analyst,
it has the default capability of looking automatically at several alter-
native assumptions.
MERGERESTIMATORrequires the same information as QUICKSCAN, plus the items listed below.
-196-
Information Required on the Acquiring Company
Item
Number used
in Exhibits
S 1(0)
Current sales estimate, this year ($M)
PAYOUT(t)
Assumed future dividend payout ratio
40%
BCR
Conversion rate, common per $100 bonds
1.0 com.
CPCR
Conversion rate, common per $100 convertible preferred
1. 0 com.
CPD
Preferred dividendrate
EPS l(t)
Future EPS estimates, next four years
$626. 0 M
7%
$ 6.50
$
7. 00
$ 7.30
$ 7.50
NOS 1(4)
E l(t)
Assumed number of shares outstanding
five years out
Dollar earnings for each of the last five years
10.0 M
$ 37. 00 to
$ 46. 00 M
S l(t)
Sales for each of the last five years
$500. 00 to
$627.00 M
Information Required on Candidate Company
S2(¢)
Current sales (estimated or actual)
$ 99.6M
S2(t)
Sales for each of the last five years
$
$
$
$
E2(t)
Earnings for each of the last five years
$ 7.4
70.0
79.2
76.6
81.2
$ 87.3 M
$ 8.2
$
. .9
$ 9.4
$ 10. 1M
BV2
Book value of assets
$144.0 M
-197-
The output from MERGERESTIIMATORfalls in three broad
classes: overall summary of preselected key data; merger results by
premium groups; and merger results by exchange-package type.
The first class of output (see Table 8-8) is an overall compar-
ative summary of selected data for each of the potential candidates.
All results are prepared on the basis of management's estimates of
"most probable" estimates of data.
The two remaining classes of output from MERGERESTIMATOR
are designed to make it possible for the analyst to examine in-depth the
financial possibilities and implications of possible merger with one or
more of the companies listed in the comparative results printouts.
Table 8-9 presents selected financial consequences that would result from each of several packages given to the acquired stockholders
under each of several assumptions as to what premium over, or dis count from, market value might be sufficiently attractive to both companies to make the acquisition possible.
This second class of output can be produced for any number of
earnings estimates the management might choose to assume for pur-
poses of analysis.
The third class of output (see Table 8-10) from MERGERESTIMATOR is less frequently used than the first two. This class of
-198-
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-20C-
information involves the collation of several series of data related to
each of several acquisition packages, taken one at a time.
These
Table 8-10-type printouts present, for each package to be considered.
several different results under each of a number of assumed possible
variations in the future earnings of the acquirer and for each of several
different levels of possible premiums.
Data derived from taking into
account synergistic effects projected to occur by management are given
in the last three lines of Table 8-10.
The MERGERESTIMATORprogram is indeed a very useful
program.
The last three lines of Table 8-10, for instance, provide a
good example of the extent to which the program provides answers to
the particular needs and objectives of the user.
Its major weakness, as far as we can tell from the description
given by the authors, is, like in the case of QUICKSCAN, to overlook
some of the other important measures of attractiveness used in acquisition analysis.
The program focuses strongly on the factors that affect
operating or business risk, but does not take the factors that affect the
financial risk of a concern into consideration.
Similar to the McKinsey4 program, MERGERESTIMATOR's
framework for analysis is entirely based on accounting procedures.
The program does not make use of the analytical techniques described
in the previous chapters, i. e., discounted cash flow analysis, probab4Op. cit.
-20 1-
0
Q.
,--
-202 -
ilistic treatment of future events, etc. Furthermore, the program
does not possess built-in capabilities for performing sensitivity analysis on future preformance. To do so, the user must rerun the model
over and over gain, using as inputs different combinations of possible
outcomes.
MERGERESTIMATOR
compares favorably relative to the McKinsey program in that:
i.
It allows the user to specify the maximum allowable
short-term EPS dilution and then computes the package which
reaches that limit.
ii.
It provides the user with more types of possible output
formats.
iii.
It may be used to structure packages which contain
convertible securities.
The programs seen thus far are intended to be used in a batchenvironment.
In what follows, we describe the ones which can be used
in a time-sharing mode. The reader is referred to the first section of
Chapter IX for a brief note on time-sharing.
-2034.
The REALSCAN Program
5
REALSCAN represents the time-shared equivalent of MERGERESTIMATOR, described in the preceding section.
The initial part of the program requires that data related to
both parent and candidate company be fed to the computer.
These data
are the base from which subsequent calculations are made. The initial
entry of these data, however, is not a firm commitment for the entire
analysis.
The manager is given several opportunities during his analy-
sis to adjust or completely change the base on which subsequent calcula-
tions are made.
Once the initial data for the parent and candidate are entered,
REALSCANallows the manager with acquisition responsibilities
to in-
vestigate one or more of the following basic merger routes:
1.
Common stock only.
2.
Common stock and convertible bonds.
3.
Common stock and convertible preferred stock.
The two additional pieces of information that can be provided by
REALSCANare:
1.
Mix of common stock and bonds to achieve specific earn-
ings dilution results.
5 David
F. Hawkins, Andrew M. McCosh, and James C. Lampe,
"Time-Shared Merger Analysis", Mergers and Acquisitions, Jan-Feb.
1969, Volume 4, No. 1
-204-
2.
Convertible preferred dividend rate required to equal
the old dividend yield on the acquired company's stock.
Under each of these alternatives,
the user is allowed to control
such variables as earnings, premium to be paid, percentage mix of
package to be offered, expected conversion of bonds or preferred stock
oustanding, dilution of earnings, and effective dividend rate desired.
The additional possibility of selecting a desired output is available. Any combination of the following print alternatives can be selected:
1.
Total package needed to be offered.
2.
Package needed to be offered per candidate share.
3.
Combined earnings.
4.
Combined EPS.
5.
Percentage dilution of earnings.
6.
Percentage
7.
Market price per share of common stock.
8.
Cash-flow per old share of acquired company.
9.
Earnings per old share of acquired company.
10.
Number of common shares outstanding.
11.
Value of common shares outstanding.
of ownership.
As mentioned, REALSCANis nothing else than the time-sharing
version of MERGERESTIMATOR. As such, it has the same inherent
strengths and weaknesses.
Clearly, however, the fact it may be used
-205 -
in the interactive mode renders it a much more practical acquisition
analysis tool than its batch counterpart.
The following table shows a sample session using REALSCAN.
-206 -
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-2 12-
5.
The PROSIM Program
PROSIM was developed to answer the question: How much is the
company to be acquired worth? Written at Harvard Business School for
use on a computer time-sharing system, the program is intended to be
primarily an educational tool which simulates the future performance of
the acquisition candidate and produces a probability distribution of its
value under various assumptions which the user can control.
More
specifically, PROSIMperforms Monte Carlo simulations to: (i) derive
pro-forma cash flows five years out and (ii) calculate a terminal value
(an analytical proxy for cash flows beyond the fifth year) which can be
based on either fifth year earnings or fifth year cash flows. The program then calculates the present value of the cash flows and of the terminal value to derive the probability distribution (risk profile) for the
value of the selling firm.
Because the program proceeds by having a dialogue with the
user, all the user needs to do is to answer the questions posed by the
program.
However, in order to avoid having to specify all the input
values in the interactive mode, it is possible to make the base data part
of the program.
Later, however, this data can be modified by retyping
a line containing the new data. While the program is running, it is still
possible to modify the discount rate or terminal value.
"Computer Programs for the Analysis of the Providence Furniture Manufacturing Company Acquisition' , Harvard Business School
Case 9-173-036, 1972
-2 13-
The probability distributions require five points from the cumu-
lative distribution. These points are entered in ascending order with
each value of the variable followed by its cumulative probability as
illustrated:
ProL,. Io
PV0L 10d
---.....
…
Less
I
I
or
5
I
I
…'
I
I
o%
I % so
. ~ .
-. 0
-20
a
I
.m
to
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··--
40
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f
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-L..
60
.
so
.
I
- LL
IO 100
-
Val e
Figure 8-1
The distribution required by PROSIM to begin simulating the
operations of the candidate firm are listed below:
Item
Acronym
CGS
Cost of good sold during first year.
GSA
General selling and administrative expenses.
WC
Working capital
G2(1)
First year growth rate
G2(2)
Second year growth rate
G2(3)
Third year growth rate
G2(4)
Fourth year growth rate
G2(5)
Fifth year growth rate
-214The following figures also need to be specified:
DPR
Five year annual depreciation
DR
Discount rate
PE
Price -earnings ratio
FSB
Fraction of shares bought initially
Two types of outputs are available from the PROSIM program:
1.
A five-year pro-forma statement of selected financial
quantities. The results are the resultant averages from 200
trials (see Figure 1).
2.
Probability distributions (risk profiles) of selected var-
iables. Figure 2 illustrates some sample output and is based
on the same data as Figure 1, with the additional assumption
of a 15 percent discount rate and an initial purchase of 80 percent of the candidate's common stock. For each variable, the
expected value or mean, standard deviation and standard error
estimate are calculated.
To the extent that PROSIM's main purpose is toteacn managers
to asses the future in probabilistic terms, the program simulates the
future operations of the selling firm by basing most of its results for
a given year on the value of sales for that year.
Furthermore,
following simple logic is embodied in the program:
the
-2 15-
1.
All probability distributions for any one year are inde-
pendent of the previous results, and of the outcome of other
quantities in the same year.
2.
The Present Value (PV) of the acquisition equals:
PV = PV (dividends) - PV (outstanding loans)
+ PV (loan interest and repayments)
+ PV (terminal value)
3.
Sales in any year is the product of the preceding year's
sales and the present year's growth rate.
4.
5.
Depreciation is straight line at $50, 000 per year.
The net value of equipment is kept constant by investing
every year an amount equal to depreciation in new equipment.
6.
If cash flow is negative, the acquirer supplies financing
at 6 1/2 interest.
7.
If cash flow is positive, the priorities are:
(i) repay
any loan from the acquirer, and (ii) if funds remain, pay
dividends.
Exhibit 1 shows the result of a typical session using PROSIM.
The critique on PROSIM has been deferred until PRODEP is described.
-216Conversation with PROSIM Program*
195 DATA .15*15*.6667
RUN
PROVIDENCE FURNITURE MODEL
BASED ON 200 TRIALS
WANT A 5 YR PRO-FORMA (1=YES.OwNO)?
VALUES IN S000
1973
1974
1975
1976
5264.8
5886.5
6444.2
6848.4
388f.7
4341
4766.1
5030.2
930.2
1026.6
1136.2
1234.5
402.9
468*.9
491.8
533.7
198.4
230.~
241.2
261.3
73.142
102
111.9
54.294
125.2
128.2
129.2
207
90.026
85.254
81.646
113.6
35.283
36.382
40.523
32.115
7.652
26.476
34.978
40.981
0-67
0.67
0.745
47.511
53.056
44.191
1972
SALES.
4719.3
CGS
3484.4
GSA
834.6
P8T
350.3
PAT
173.2
ADD W.C.
-2.657
CASH FLOW
175.9
DIVIDENDS TO DRA
92.585
LOAN FROM DRA
9.974
LOAN REPAYMEN
IT
0
PRBO OF DIVIDEND PAYMIENT
0.865
0.74
OUTSTANDING LeAN
9.974
37.606
WANT JUST NPV CO), OR ALL 6 PROFILES
)?O
NPV
MEAN
STD DEV
STD ERR EST
0 %TILE
2249.7
1196.9
84.6
-611.2
50 2TILE'
75 TILE
100 TILE
2384.0
3196.4
5414.8
25 %TILE
1519.6
*User responses are underlined:the data supplied to the
program is the same as in Figures 1 and 2 with the assumption
that DRA buy 2/3 of the Providence stock initially.
-2 17TERMINAL VALUE CALCULATION IS
BASED
N 15 TIMES YR 5 EARN.INGS
WANT MORE C(=YES.O=NO)?l
WHICH OPTION
NONE
(0)
00D YOU WANT?
CHANGE DISCOUNT RATE (1)
(2)
CHANGE P/E MULTIPLE
CHANGE CASH FLOW MULTIPLIER
CALCULATE TERMINAL VALUE
BY P/E MULTIPLIER
(4)
OR BY CASH FLOW
(5)
(3)
?.L
CURRENT CASH FLeW MULTIPLIER IS 6.66667 WHAT IS NEW VALUE?20
OPTION NO.?,
TERMINALVALUE IS NOW 20 TIMES YR 5 CASH FLW
OPTION NO.0O
WANT A 5 YR PRO-FORMA CIwY£S.O0NO)?O
WANT JUST NPV
(O),
OR ALL 6 PROFILES
Ct)?J,
0NLy RISK PROFILE SUMMARY CO), OR PERCENTILES TOO Cl)?0
TERMINAL
VALUE *
NPV
MEAN
STO DEV
YR 5
PAT
AV YR4
YR5 PAT
YR 5
SALES.
2189.3
3829.0
1903-7
259.6
243.Q
6844.3
2511-
4901.7
2437.0
153.7
118.4
452.
346.6
172.3
10.9
177.6
STD ERR EST
TERM VAL
DISCOUNTED
8.4
32.0
* BASED ON 20 TIMES.YR 5 CASH FLOW
WANT MRE
WHICH
?2
CIlYESO=N)?!
PTION DO YOU WANT?
CURRENT VALUE OF P/E MULTIPLE IS 15 WHAT IS NEW VALUE?80
OPTION NO.?4
TERMINAL VALUE IS NOW 20 TIMES YR 5 EARNINGS
OPTION N?0O
WANT A 5 YR PRO-FORMA CIzYESO=NO)?_
0R ALL 6 PROFILES
WANT JUST NPV (0).
C1)?L
ONLY RISK PROFILE SUMMARY CO() OR PERCENTILES TOO (1)?l
NPV
TERMINAL
VALUE *
TERM VAL
DISCOUNTED
YR 5
PAT
AV YR4
YR5 PAT
YR 5
SALES.
MEAN
2922.2
5311.0
2640.5
265.-
244.4
6795.1
STD DEV
1540.4
3004.7
1493.8
150.2
100.2
410.3
108.9
212.5
105.6
10.6
-2124.0
1881.5
3082.6
3927.3
7283-.7
-4590.5
3210-8
5564.6
7328.8
13701.9
STO ERR EST
0
25
50
75
100
TILE
TILE
TILE
TILE
TILE
* BASED ON 20
WANTMRE
-2282*3
1596.3
2766.6
3643.7
6812.3
-229.5
160-.
278.2
366.4
685.1
7.1
-21.7
177.6
255.3
314.7
490.2
29.0
5898.4
6481.1
6773.7
7041.9
7766.
TIMES YR 5 EARNINGS,
ClwYES1oC~xN9)9_o
(C ont inue d on P. 2 2 1)
PAGES (S) MISSING FROM ORIGINAL
PAGES (S) MISSING FROM ORIGINAL
PAGES (S) MISSING FROM ORIGINAL
-22 1-
6.
The PRODEP Program
8
PRODEP (Pro Deal Evaluation Program) is an interactive computer program which uses the output of PROSIM and performs an analysis of the possible cost in present value terms to the acquirer or the
various financial packages which might be offered to the acquisition
candidate.
The program assumes the case of a contingent payment,
i. e., that the package will consist of an initial cash payment followed
by a payment at the end of five years based on a multiple of some inter-
imperformance measure. The program automatically considers fifth
year earnings, the average of fourth and fifth year earnings and fifth
year sales as possible measures. The output of the program is designed to answer two questions:
1.
If the acquisition has a mean present value of $X, and
if $Y is paid initially (i. e., NPV = $Y + $X), what multiple of
each performance measure is implied for the payment to be
made at the end of five years,
in terms
of
a.
All of the acquisition's outstanding shares.
b.
The shares of the acquirer will buy in the fifth
year.
2.
If $Y immediate
cash if offered now, and the payment to
be made in the fifth year is set to be equal to a predetermined
8 Idem.
-222 -
multiple of the performance measures,
what is the probability
distribution (along with its mean) of:
a.
That payment undiscounted.
b.
That payment discounted.
c.
The total package discounted
For illustration purposes, assume that the payment to be made
during the fifth year is made contingent upon the amount of earnings for
that year, and that the acquisition has a mean present value of $2, 000, 000
of which $1, 000, 000 is paid now in cash.
If it is determined that the expected value of fifth year earnings
is $191,200 (not discounted), the program determines the multiple by
which this figure when multipled has a present value of $1, 000, 000
(i. e., what payment will yield NPV = 0?).
This is determined as
follows:
Future
Multiple
value of $1, 000, 000 = $ 1 x ( 1. 15) 15 = $2. 01 Million
= Future value of $1,000,000
Mean earnings fifth year
$2. 01
$. 1912
The cumulative distribution fractiles of the fifth year earnings
distribution are then multiplied by 10. 52 to obtain the distribution of
the contingent payment. The values of this distribution are then dis -
-223 counted into the present and added to the initial $1, 000, 000 cash payment to obtain the probability distribution of the whole package.
The obtained multiple (10. 52) represents the multiple which,
if attached to fifth year earnings, yields an expected net present value
of zero for the acquisition.
This means that, based on the probability
distributions specified for PROSIM,if a higher (lower) multiple is affixed to fifth year earnings in determining the contingent payment to be
made in that year, the acquirer will pay an amount which on a present
value basis yields a NPV for the acquisition lower (higher) than zero.
Therefore,
10. 52 represents the highest P/E multiple that the acquirer
should affix to fifth year earnings in determining the value of the contingent payment.
In order to use PRODEP, it is necessary to run PROSIM so as
to obtain the distributions for the three performance variables to be
used in determining the value of contingent payment.
Once the program is running, the discount rate, the amount of
initial payment, and the percentage of stock that this initial payment
will buy (i. e., the price at which the stock will be bought) can be varied.
Other measures of performance, besides fifth year earnings,
the average of fourth and fifth year earnings, and fifth year sales, can
be used.
-224The program's logic is extremely simple: it simply performs
a rescaling of probability distributions of performance measures based
on multipliers and discount factors.
It presumes that if the perform-
ance measure on which the fifth year payment is based, is negative, no
payment will take place by either party.
Exhibit 2 shows the result of a typical run using PRODEP.
The PROSIM and PRODEP programs deal with risk in a systematic and formal manner.
Both programs have been developed for edu-
cational purposes (they have both been specially tailored for use in
classroom sessions at Harvard Business School), and accordingly, are
easy to get acquainted with and to use. The concept of risk and its im-
portance in acquisition analysis are clearly demonstrated. The educational strong points of PROSIM and PRODEP have been obtained, however, at the inevitable expense of rigidity and simplicity of logic, facts
which may become serious liabilities in real-world applications (e. g.,
single and constant discount rate to compute PV, independence of cash
flows fromperiod to period, single lending interest rate, automatic
lending by the acquirer in case of negative cash flows). Nevertheless,
the approach used can easily be incorporated into acquisition simulation programs of the MERGERESTIMATOR-type. The next program
to be described constitutes an effort in that direction.
-225Conversation with PRODEP Progrant
DEAL EVALUATION PROGRAM FOR
PROVIDENCE FURNITURE ACOUISITION
CURRENT
DISCOUNT
RATE IS 15
NEW RATE?1.
INPUT TOTAL EXPECTED NPV
WANT TO CHANGE
F DEAL YU
IT ¢C=YES,OuNO)?j.
ARE OFFERING
C IN S 000 )?2315o7
HOW MUCH OF THAT WILL BE IN CASH NW?.8
WHAT PERCENT
F THE SHARES WILL THAT AMOUNT 8UY?JB
MULTIPLIERS THAT APPLY TO THE WHOLE COMPANY
FOR THE PAYMENT AT THE END OF YR 5 ARE:
YR S EARNI.NGS
AVERAGE EARNINGS
YR 5 SALES
MULTIPLIERS
YR 4
2.80
2.93
YR 5
0.11
RESTATED
YR 5 EARNINGS
AVERAGE EARNINGS
YR 5 SALES
IN TERMS OF REMAINING
YR 4
.50
.75
1.00
MEAN
DIST. OF TOTAL PAYOUT
PRESENT VALUE
0.
290.032
824.7
512.074
1142.4
1871.1
798.684
709.341
1161.81
495.92
AT 3 TIMES AVERACE EARNINGS YR 4 YR 5
CUM PROS
VALUE IN YR 5
PRESENT VALUE
.00
0
0
.25
.50
508.8
788.4
315.925
489.534
·75
983.4
610.614
1715.7
763.786
1065.31
474.251
1.00
MEAN
AT
0.15
CUM PROB
.00
TIMES YR 5 SALES
PRESENT VALUE
VALUE IN YR 5
*S25
842.835
981.66
523.334
609.534
.50
1023.5
635.51
.75S
1.00
1076.4
668.36
1193.
1027.26
637.848
MEAN
F THE SHARES
t(1YES*OuNO)?1
THE WHOLE
F YR 5 PAYOUT
AT 3 TIMES YR 5 EARNINGS
CUM PROB
VALUE IN YR 5
.00
0
.25
467.1
Z
14.01.
14.65
0.54
YR 5
WANT TO CHANGE ANY F THE MULTIPLIERS
INPUT THE 3 MULTIPLIERS THAT APPLY T
COMPANY IN THE SAME ORDER AS ABOVE
?3.3..15
DISTRIBUTION
20.
740. 756
*User responses are underlined.
PRESENT VALUE
1852.56
2142.59
2364.63
2561.9
3014.37
2348.48
PRESENT VALUE
1852.56
2168.48
2342.09
2463.17
2917.87
2326.81
PRESENT VALUE
2375.89
2462.09
2488.07
2520.92
2593.32
2490.41
ARF:
-22 6IS THAT ENOUGH (1=YES,O=N0)?Q
CURRENT DISCOUNT RATE IS 10 tX WANT TO CHANGE
IT (=YES,ON0)?.L
NEW RATE?15
INPUT TOTAL EXPECTED NPV OF DEAL YOU ARE OFFERING
( IN S 000 )?2300
HOW MUCH OF THAT WILL E IN CASH NW?.6
WHAT PERCENT OF THE SHARES WILL THAT AMOUNT BUY?66.7
MULTIPLIERS THAT APPLY TO THE WHOLE COMPANY
FOR THE PAYMENT AT THE END F YR 5 ARE:
YR 5 EARNINGS
AVERAGE EARNINGS
YR 5 SALES
MULTIPLIERS
YR 4,
0.27
RESTATED
YR 5 EARNINGS
AVERAGE EARNINGS
YR 5 SALES
6.95
7.27
YR 5
IN TERMS OF REMAINING
33.3
2 OF THE SHARES ARE:
20.87
21.83
0.81
YR 4, YR 5
WANT TO CHANGE ANY OF THE MULTIPLIERS (I=YES,OxNO)?1
INPUT THE 3 MULTIPLIERS THAT APPLY TO THE WHOLE
COMPANY IN THE SAME ORDER AS ABOVE
?7. 7.5,.30
DISTRIBUTION
AT
7 TIMES YR 5 EARNINGS
CUM PROB
VALUE IN YR 5
.00
0
.25
1089.9
.50
1924.3
.75
1.00
MEAN
DIST. OF TOTAL PAYOUT
OF YR 5 PAYOUT
PRESENT VALUE
0
541.873
956.717
2665.6
4365.9
1863.6
1325.27
2170.62
926.536
AT
7.5 TIMES AVERAGE EAIRNINGS YR 4 YR 5
PRESENT VALUE
VALUE IN YR 5
CUM PROB
0
.00
0
1272.
632.409
.25
1971
979.935
.50
1222.31
2458.5
.75
1.00
4289.25
MEAN
1909.46
AT 0.3 TIMES YR 5 SALES
VALUE IN YR 5
CUM PROB
1685.67
.00
1963.32
.25
.50
2046.99
.75
2152.8
1.00
MEAN
2132.52
949.342
PRESENT VALUE
838.076
976.117
2385.99
2054.52
IS.THAT ENOUGH (1=YESO=NO)?0
1017.72
1070.32
1186.26
1021.46
PRESENT VALUE
1380
1921.87
2336.72
2705.27
3550.62
2306.54
PRESENT VALUE
1380
2012.41
2359.94
2602.31
3512.52
2329.34
PRESENT VALUE
2218.08
2356.12
2397.72
2450.32
2566.26
2401.46
-227CURRENT DISCOUNT RATE IS 15 2. WANT TO CHANGE IT (1YESIO=NO)?O
WANT T CHANGE THE DEAL t1=YES.O=N0)?L
INPUT TOTAL EXPECTED NPV
F DEAL YOU ARE OFFERING
C IN S 000 )?2300
HOW MUCH OF THAT WILL BE IN CASH NW?.35
WHAT PERCENT OF THE SHARES WILL THAT AMOUNT BUY?51
MULTIPLIERS THAT APPLY T
FOR THE PAYMENT
THE .I4MLECOMPANY
AT THE END OF YR 5 AREs
YR 5 EARNINGS
AVERAGE EARNINGS
YR 5 SALES
YR 4
11.29
11.81
0.44
YR 5
MULTIPLIERS.RESTATED IN TERMS OF REMAINING 49 . OF THE'SHARES ARE:.
YR 5 EARNINGS
23.05
AVERAGE EARNINGS
YR 5 SALES
YR 4
YR 5
24*10
0.90
WANT TO CHANGE ANY OF THE MULTIPLIERS (I=YES.O=NO)?O
DIST. OF TOTAL PAYOUT
DISTRIBUTION
OF YR 5 PAYOUT
AT
TIMES YR 5 EARNINGS
11.2948
CUM PROB
VALUE IN YR 5
PRESENT VALUE
.00
*25
.50
0
1758.59
3104.93
0
874.332
1543.7
.75
4301.04
2138.38
1.00
7044.54
3502.38
MEAN
3006.98
1495
AT
11.8108 TIMES AVERAGE
CUM PROB
VALUE IN YR 5
.00
EARNINGS.YR
PRESENT VALUE
805
1679*33
2348.7
2943*38
4307.38
2300
4. YR 5
PRESENT VALUE
PRESENT VALUE
805
0
0.
.25
.50
.75
1.00
2003.11
3103.88
3871.59
6754.61
995.902
1800.9
1543.18
1924.86'
3358.23
2348.18
2729.86
4163.23
MEAN
3006.98
1495.
2300.
AT 0.439078
TIMES YR 5 SALES
CIJM PRMB
VALUE IN YR 5
PRESENT VALUE
1226.6
.00
2467.13
.25
.2873.5
1428.64
.50
2995.96
1489.52
.75
3150.82
1566.51
1.00
3492.12
1736.2
MEAN
3006.98
1495.
PRESENT VALUE
2031.6
2233.64
2294.52
2371.51
2541.2
2300.
-2287.
The Corning-Glass Works (CGW)Program
9
The CGW program was developed to:
1.
Aid in computing the "best" or "acceptable" cash price
of acquisition candidate, taking into account its past and future
(projected) performance.
2.
Provide the implication of various prices on the acquirer's
EPS, ROI, and P/E ratio.
3.
Provide estimates of the effect on the acceptable price
due to errors in estimates and/or assumptions (Risk and Sen-
sitivity Analysis).
The model performs primarily accounting-type computations to
get cash flows and then calculates ROI and other specified criteria.
can be run as a risk-analysis,
It
as a deterministic or most likely estimate
and sensitivity analysis model. In practice, the risk feature is utilized
only in the last stage of computations, with most of the analyses being
performed for the best estimates for sensitivity analyses, and to answer various "what if" questions posed by management, such as effects
of changes of purchase price on a financial measure, or vice versa.
The basic types of estimates used in the evaluation are determined by reviewing past financial statements of the acquisition candidate,
and through interviews with its management.
9 John
They include:
C. Chambers and Satinder K. Mullick, "Determining the
Acquisition Value of a Company", Management Accounting, April 1970,
pp. 24-39.
-22 9-
* Net sales
* Cost of sales in dollars or as a percent of sales
* Selling, general and administrative expenses
R and D
* Other income
* Past and future capital requirements
* Last three years' depreciation and amoritzation estimates
* Value of undepreciated assets
* Interest and other expenses
* Working capital and inventory requirements
* Short- and long-term debt
* Taxes, etc.
The CGW program is flexible enough so that the amount of detail
incorporated in the model depends on the available data and the accuracy
of detailed versus gross estimates.
As in the PROSIM program (described in Section 4. 4), the risk
analysis is performed by (i) specifying a cumulative probability distri bution for one or more input variables,
(ii) performing a series of
Monte Carlo trials to get the corresponding probability distribution
for ROI, or some other measure.
An important extra feature of the
CGW model is to allow variables to be dependent upon each other.
-230In order to calculate the present value of the acquisition candidate, the CGW model requires that the acquirer first use the model to
determine his own ROI probability distribution function, and then use
the distribution mean as the appropriate discount rate to be applied
against the acquisition's projected cash flows. According to the authors,
this approach ensures that both firms will be evaluated on the same
basis.
Once the present value of the acquisition candidate is computed,
its number of outstanding shares determines the maximum price at
which the shares should be traded or bought.
The CGW program can equally well be used to determine the effect of a type of transaction
on (i) the EPS of the acquirer,
dividends to be paid to the acquired stockholders.
and (ii) the
For this purpose, the
program has the capacility of examining the effects of any package con-
sisting of common, convertible preferred stock, warrants, and convertible debentures.
As in most of the preceding cases, the set of viable
exchange packages (i. e., packages that satisfy the minimum stated objectives of management) must be determined by a trial-and-error
pro-
cedure.
The CGW acquisition analysis program is indeed a more sophisticated version of PROSIM: It performs the same kind of risk-analysis
whilst allowing the user to (i) specify a much wider set of assumptions
-23 1-
about the future, and (ii) use his own accounting rules.
However, the
application of the acquirer's discount rate against the acquisition's
projected cash flows constitutes a serious financial mistake (unless the
acquisition belongs to the same risk class as the acquirer).
We have
already seen that the appropriate discount rate to be applied is the acquisition's cost of capital p.
-232 8,
The COMMAND Program
10
Developed by First National City Bank, the COMMAND(Com-
puter Assisted ManagementDecisions) program is a time-sharing
designed to provide management with a tool for (i) divisional or corporate forecasting, (ii) planning, and (iii) acquisition analysis.
Conceptually, COMMANDis an automated accounting framework of any company, division or plant. The user must provide for
each accounting entry his best estimate for the current year's level,
and future growth rates.
COMMANDis made up of six modules, each of which performs
a different type of financial analysis.
Although most of these modules
may be used for the analysis of a subsidiary, a division or an acquisition candidate, their description will be given solely in terms of their
relation to acquisition analysis.
1.
PASTFLOW
This module, generally the first step in the analytical
process, produces a complete trend analysis and operating
ratio analysis of at most, twelve past accounting periods(either
months, quarters, or years). The program serves three
funct ions:
1 Leonard
N. Druger, "Computer Time-Sharing Aids in Forecasting", Financial Executive, August 1972, pp. 20-23.
-233-
a.
It serves as a point of reference to the corporate
manager while he formulates assumptions for a forecast.
b.
It focuses attention on adverse operating trends.
c.
It highlights any inconsistencies between the ac-
quisition candidate's forecast and its past performance.
2.
CASHPLAN
The module takes the user's assumptions about the future
and generates a complete twelve-period forecast including income statement, balance sheet, ratio analysis, source and uses
of funds statement, reconciliation of working capital, capitaliza-
tion analysis, cash-flow statement, and a list of the assumptions
that produced the forecast. The system provides several methods of forecasting each component of a corporate balance sheet
and income statement.
3.
EDIT
EDIT checks the assumptions entered into the CASHPLAN
forecasting program for mechanical consistency and correctness.
4.
PRODPLAN
Instead of basing the acquisition candidate's forecast
purely on overall revenue estimates, the user may go downto
the product-line level and input the price, volume, fixed and
-234-
variable cost per unit for any number of product lines.
The
resulting composite sales and costs are automatically fed into
CASHPLANwhich produces up to eight traditional financial
reports.
PRODPLAN enables the manager to measure the
impact of a change in product mix, volume, price or unit cost
on the total earnings and cash flows of the acquisition candidate.
5.
MERGE
MERGE is used to consolidate, either on a pooling or
purchase method of accounting, the financial data of the acquirer
and proposed acquisition.
The analyst can introduce any com-
bination of specific alternatives for financing the acquisition.
MERGE produces a complete financial profile of the new con-
solidated entity.
6.
TARGET
This module takes the acquirer's established earnings
objective for each of the next five years and compares them
with the earnings expected from existing business activities.
The difference, if any, represents the earnings gap that must
be satisfied by new investments, new products, or acquisitions.
Then, based upon leverage and liquidity constraints,
a plan is
established for financing both normal business activities and
the required external investment.
-235TARGET calculates the amount, timing, and types of sources
(how much should be debt, how much equity) for the required investment. It also prints out a complete eight-page pro-forma financial
picture of the acquirer meeting its objective.
COMMAND
is instantly accessible from a standard telephone
anywhere in the United States, Canada, or Europe.
Information en-
tered into the system is protected through a security system.
COMMAND
represents a very powerful time-sharing system
for forecasting, financial planning, acquisition analysis and consolidation, product-line planning, and policy decision evaluation.
All of
these functions are performed simply by simulating the future activities
of a firm and by translating results into accounting and financial analysis statements.
To the extent, however, that the system lacks the
more sophisticated techniques for dealing with risk, for performing
present value analysis, andforperforming sensitivity analysis, it
represents a rather clumsy and costly tool for doing acquisition
analysis.
-2369.
The RAYTHEON Program 1
Developed by Robert Seaman in 1968, the RAYTHEONprogram
is designed to investigate in an interactive mode the impact that a pro-
spective acquisition's operating results have on its financial results.
Accordingly, the program is capable of (i) accepting relevant opera-
tional, market and financial data, (ii) generating detailed quarterly
performance results for the next three years, (iii) processing substitute values in a variety of functions in a "what if" mode, and (iv) test-
ing the profit sensitivity to sales levels.
The model is conceived of mathematical expressions for each
of the sales, cost, balance sheet, and cash flow items normally associated with the measurement of operating and financial performance.
All constants assigned to such expressions can be changed at any
moment by simply typing the new values at the terminal keyboard.
The simulator program accepts the changes and immediately recomputes all affected values throughout the model. Upon command, the
results of these revisions are displayed for further consideration by
the user.
At the end of each simulation exercise, a sales sensitivity test
of the break-even point can be made. Also, the program displays for
11Robert L. Seaman, A Simulation Approach to the Analytical
Aspects of Business Acquisition Evaluation, Unpublished Master's
Thesis, Sloan School of Management, M. I. T., June 1968.
-237-
the user the circumstances of all revisions made to the model's mathematical formulations.
The output of the model consists of the following reports and
stat ements, given by quarter-year periods and-year totals for three
future years:
1.
Operating results.
2.
Balance sheet statements.
3.
Source and application of funds statements.
4.
Consolidated reports for parent and acquisition.
The inputs to the model include forecast of:
1.
Operating Items
· Sales
· Manufacturing costs (variable, fixed, other)
* Operating margins
·General, selling and administrative expenses
· R and D expenditures
2.
(new product and existing)
Balance Sheet Items
* Current Assets
* Plant and equipment
* Other non-current assets
* Current liabilities
Long-term debt
Owner Equity
-23 8-
3.
Cash Flow Items
Depreciation
· Investment in plant and equipment
* Loan proceeds and paybacks
Other sources and applications
Working capital and requirements
The RAYTHEONprogram for acquistion analysis explores in
depth the operational aspects of a prospective acquisition.
It does this
in a manner which provides a great degree of flexibility to the user. Its
overall scope, however, is very limited. The program fails to provide the user with (i) many of the elements which are important in ac-
quisition analysis (financial ratios, per share data, etc. ), and (ii) the
means of determining a price for the acquisition.
-239-
C.
The Relationship of the Programs to Our Framework of Analysis
of the acquisition analysis,
One of the main characteristics
framework presented in Chapter VI, is the iterative nature of the computations.
This feature makes the computer a nearly indispensable aid
to the manager performing the analysis.
In this section, we attempt to
indicate where and how the several programs described so far may be
used. Instead of referring to each program individually and indicating
in which phase of the analysis it may be used, we shall do the inverse,
i. e., we shall refer to a step of the analysis and indicate which programs may apply as aids.
To the extent that most programs are noth-
ing other than accounting simulators,
their main use is to project the
future cash flows required to determine the fair market value of the
prospective acquisition. Furthermore, because the programs generate
the future balance sheets and operating statements of the company, their
results may be useful in indicating to the buyer what adjustments to
the price and package to be offered may be required to bring the future
financial results in line with his objectives.
1.
Projection of the Acquisition's Future Cash Flows
To project the future performance of the prospective
acquisition, there are two types of programs: (i) those which
perform the pertinent simulations in a deterministic fashion,
and (ii) those which use the Monte Carlo approach to derive
-240-
the probability distributions of future cash flows. In the first
group, we have the COMMAND, CGW, McKinsey and RAY-
THEON programs, their order of citation being that which we
attribute to their capabilities and degree of sophistication.
In
the second group, the relevant programs are, in order of
capability, the CGW and PROSIM programs.
To the extent that these programs simply extrapolate
into the future the present performance and financial status of
the firm, according to the best estimates of management, the
projected cash flows can be made to include any synergistic
benefits accruing from the consolidation by inputting higher
estimates of future performance.
2.
Determination of the Acquisition's Fair Market Value
Once cash flows have been estimated
for a number of n
years into the future, the fair market value of the firm is determined by discounting the cash flows and the terminal value of
the firm at the risk-adjusted rate of return r required by the
market. The only programs which perform present value analysis on the projected future cash flows are PROSIM and CGW.
The first of these is rather limited in its real world applications
as it is conceived to be primarily an educational tool. CGW,
on the other hand, is quite flexible insofar as the user's
-24 1-
assumptions and requirements are concerned, and may, therefore, constitute a useful aid both to perform the projections of
future cash flows (in a deterministic or probabilistic fashion)
and compute the present value of those cash flows. It is important, however, that the analyst not use the discount rate
computed by the program 1 , but input the appropriate discount
rate as is determined in Chapter III.
3.
Adjustments
to the Maximum Price Before Taxes
Because most programs generate pro-forma balance
sheets, operating and use-of-funds statements of the consolidated company, their practical use is more directed at helping
managers evaluate an acquisition in terms of its "book impact"
than at determining its addition to the value of the firm.
This
confirms what is discussed in Chapter IV, namely, that issues
such as resulting EPS, debt-to-equity ratio and amount of retained. ownership are usually given considerable attention in
evaluating the attractiveness of a prospective acquisition.
In this context, the programs which are useful in performing this type of analysis are COMMAND, REALSCAN,
MERGERESTIMATOR and McKinsey program.
1The program uses the acquirer's
the discount rate.
expected rate of return as
-242 D.
Comparison of Programs
To the extent that a description has been provided for each
program, the best way to contrast them is through a concise listing
of their major characteristics.
This is done below:
Table 8-14
Functional Characteristics of the Programs
I
F
'described in Chapter IX
-243 CHAPTER
IX
The FUSION Program
In this chapter, we describe a computer program which we
designed to perform a function that none of the previously reviewed
programs does, namely that of being able to structure a merger
package according to management's specifications about desired future
financial performance for the consolidated company.
The first section of the chapter gives general considerations
about time-shared acquisition analysis and describes some of the advantages of interactive programs as compared to batch ones. The
second section, describes the scope and domain of applicability of
FUSION, and relates its functions to the acquisition analysis framework proposed in Chapter VII.
In the third section, we describe FUSION's input requirements
and illustrate how the program is to be used; the chapter continues
with an evaluation of the program as a whole, and with suggestions
for improvement.
In Appendix G,
sample session using the program.
we include the output of a
-24 4-
A.
A Note on Time-Sharing
Acquisition Analysis
Time-sharing is an option available on the majority of third
generation computers which gives several users the ability to use
the computer simultaneously.
Although the computer services each
connected user in turn, it does it so rapidly and in such small time
segments that each user has the impression that he has the machine
all to himself.
The user communicates with the computer through a remote
terminal, which may be a simple teletypewriter or a more sophisticated visual display (CRT) unit resembling a television set. The
terminal permits the user: (i) to insert data or programs into the
computer; (ii) to call upon data or programs already stored on tape
or disk; and (iii) to perform other manipulations of data as required.
When a user is connected in a time-sharing
mode with a com-
puter, and if a suitable program is available for use, he may carry on
a "conversation" with the computer.
This makes it possible for him
to combine his talents as a decision-maker with the calculating power
of a computer.
In the context of acquisition analysis, this conversational
mode has several advantages:
i.
Instead of being required to put together all the input
information at once, as is the case with batch processing, the
-245user can change input information as his calculations proceed.
Time-sharing programs are designed to request information
input from the manager immediately before it is needed. In
this way, the manager need not make decisions until they are
absolutely necessary.
ii.
The multiplicity of alternative
ways to acquire a com-
pany and the variety of variables to be taken into account,
usually lead members of management, in the course of a merger review, to ask questions beginning with: "What would
happen if ...
?" These "what if" questions require fast
answers. Using a time-sharing program, the manager or analyst to whom such question are addressed can type at the ter-
minal the appropriate request and obtain an answer within
second.
iii.
By experimenting with a variety of operating and fin-
ancial estimates for the parent and candidate companies, a
manager has the opportunity of establishing complete famil-
iarity with the range of possible implications that the acquisition may entail.
The flexibility which time-sharing puts a
his disposal, enables the manager to gain this precious insight
in a much shorter period of time than otherwise required.
-24 6-
iv.
To the extent that time-sharing programs are easier
to learn and write than batch-processing languages, it is
possible for an executive to rapidly acquire proficiency in
programming and so create his own programs without having
to interface with the company's computer staff. Since he himself is the one most familiar with analytical methods and ob-
jectives, this programming capability permits him to generate
programs faster and with fewer interpersonal problems. Also,
this freedom allows him to experiment with new and different
analytical techniques since he can test a technique as soon as
he programs it.
B.
Introduction to FUSION
The purpose of FUSION is to help management determine the
attractiveness of an acquisition and structure the acquisition payment
package.
FUSION will (i) assist in forecasting the future earnings of
the acquiring and selling companies, (ii) determine from among the
available financing media the mix of securities to be used as payment
which best fits into the acquirer's short- and long-range financial plans,
and (iii) help in analyzing the financial impact of the acquisition.
To assist in forecasting future earnings,- FUSIONrequires
as inputs the current estimated and past five years' earnings, net of
any extraordinary items. The program then fits through the data the
-24 7-
curve which best "explains" the past, and uses it as a proxy to project
income for the next five years.
The analyst is free, of course, to use
these projections or to generate his own estimates in analyzing the impact of the acquisition upon the parent company.
In order to be used as a package structuring tool, FUSION requires that the types of financing media to be used as payment be specified. The available options include cash, common stock, convertible
preferred shares and bonds. The information required for the options
includes the interest or dividend rate, the conversion ratio and sinking
fund requirements.
The user is then given the choice of either specifying the mix
of securities in the package, or letting the program do so. Whenthe latter
alternative is chosen, FUSION makes use of the goal programming technique described in Chapter VII and requires the manager to specify his
subjective estimates of the intangible costs associated with not attaining his goals.
FUSION then determines the financing package which
meets the corporation's goals at the lowest cost.
To help in analyzing the financial impact of the acquisition,
FUSIONsimulates the future performance of the consolidated firms
for four years into the future.
-24 8-
The outputs from the model include the (i) regression coeffi-
cients of best fit curves used for forecasting future income, (ii) estimated after-tax financial results for the next four years, (iii) proposed transaction package, and (iv) tables for testing the sensitivity
of the package solution to changes in the goals and constraints.
C.
Using FUSION
This section illustrates the applicability
of FUSION1 and
describes how the program can be used.
As is the case for most time-shared programs, a session is
initiated by establishing a telephone connection with the computer and
by identifying oneself to the computer.
From then on, the program will ask the operator for the required input information at each step of the analysis.
All questions
are asked in plain English language. With the aid of a short pamphlet
of instructions, the user is simply required to type all the pertinent
data at the terminal.
For most purposes, the user need not have
any proficiency in programming to run the program competently.
To conclude a session the user must simply type a zero (0) when the
program asks him the question "WHATNOW?" or alternatively, press
the ATTENTION button on.the terminal at any point of the analysis.
1The program presented here does not constitute what we
envision to be the final version of FUSION.
-24 9-
The initial part of the program requires that data related to
both the acquirer and prospective acquisition be fed to the computer.
These data are the base from which subsequent calculations are made.
The information required for each company includes:
i.
Past five years' earnings history
ii.
Current year's estimated earnings.
iii.
Number of outstanding shares.
iv.
Market value of shares, if any.
v.
Book value of shares.
vi.
Long-term debt outstanding (book value)
vii.
Working capital balance.
The initial entry of these data is not a firm commitment for
the entire analysis. The user is given several opportunities during
the analysis to adjust or completely change the base data.
Once the companies' data has been entered, the program allows
the user to investigate the impact of acquiring the candidate firm with
cash and/or any combination of the following types of securities:
i.
Common stock
ii.
Convertiblepreferred
iii.
Bonds
iv.
Cash
-250The user is then asked to either specify the mix of securities
to be issued or to specify the set of goals and associated implicit
costs which he wishes the package to achieve.
Under each of these alternatives, the user is allowed to control
influencing variables such as earnings, premium to be paid, percentage
mix of package to be offered, expected conversion schedule of the preferred stock issued, dilution of earnings, and effective dividend rate
desired.
The output of the program includes:
i.
Package needed to be offered.
ii.
Combined earnings.
iii.
Combined earnings per share.
iv.
Earnings per share issued.
v.
Percentage dilution of earnings.
vi.
Resulting percentage ownership.
vii.
Resulting capital structure
viii.
End of first year working capital balance.
-251D.
Evaluation of FUSION
Drawing upon the ideas and formulation presented in Chapter VII,
FUSION was designed with the main objective of allowing a manager
to structure rapidly the package of securities to be used as payment
for an acquisition. For this purpose, the program was originally
provided with the capability of translating the manager's specified
deviation penalties (usually dollars per percentage point of deviation)
into the internal goal programming penalties.
This proved to be im-
practical for two reasons:
i.
It is extremely hard for a manager to attach a dollar
value to a percentage point of EPS, ownership or debt-to-equity
ratio deviation from target.
As a result, the manager can at
most specify which deviations he regards as highly unfavorable
and accordingly attach to them very high penalties (i. e., make
the goal become a "hard" constraint).
ii.
Because the user does not know what conversion factors
are being applied to his penalties in order to convert them into
internal penalties, he loses the capability of balancing his
several objectives.
In order to remedy these shortcomings, FUSION's internal logic
was "exteriorized",
that is, all questions were modified to allow the
manager to attach his penalties to the interior deviations (which in most
-252 -
cases are expressable in dollars). This modification considerably improved the effectiveness of the program.
Because in its present stage of development, FUSION is not set
up to perform multi-period analysis (for example EPS growth is not
taken into consideration), most goals are usually exactly met by entering convertible preferreds into the proposed package solution.
Inas -
much as convertible preferred stock does not dilute the immediate EPS
or the degree of retained control as much as common stock, nor does
it adversely affect the debt-to-equity ratio as much as debt, it usually
replaces any excesses of stock or of bonds in the final solution.
Experience with FUSION has revealed that, although no computer
experience is required from the user, it is necessary to possess a working knowledgeof linear programming and of sensitivity analysis to derive
the maximum use of the program.
This fact indicates that much of the
future work to be invested in developing FUSION should go into render-
ing it a more practical tool for users not acquainted with the program's
internal analytical techniques.
Apart from these comments, which have been directed at
FUSION's package determinator subroutine, we think the other sub-
routines require further development. Specifically:
i.
The input/output subroutine should be rendered more
flexible.
-25 3-
ii.
The program should be provided with a discounted
cash-flow package.
iii.
The user should be allowed to assess future outcomes
in probabilistic terms.
iv.
The overall accounting framework of the program should
be rendered more flexible.
-254CHAPTER X
Summary and Suggestions for Further Research
Throughout this thesis, we have examined what methods, techniques and computer-aids can be used to assess the value of a prospective acquisition.
To increase the scope of our study, we chose to deal
with companies which are privately-owned, that is, companies for
which a market value is not known. This led us to the general problem
of estimating the fair market value of a firm.
Once this issue was examined, we entered the main subject of
this thesis:
how a buyer may determine the price to be offered for a
prospective acquisition.
A survey of the literature on mergers and
acquisitions revealed that the techniques commonly used imply
that many firms center their financial analysis on the impact that the acquisition will have on their books. Several of the issues
which are usually considered when determining the purchase price of
an acquisition candidate were discussed.
We then examined the valuation approaches that financial theory
suggests for acquisition analysis purposes, and found that in essence,
the approaches proposed are the same as those used to evaluate internal investment projects, i. e., discounted cash flow and portfolio
analys is.
-255Using this framework of analysis and recognizing the fact that
the synergistic effects generated by a merger usually make an acquisition worth more to a buyer than its fair market value as a separate
entity, we examined ways by which the synergistic benefits expected
to accrue from the consolidation may be valued. Specifically, we
proposed a framework of analysis which focuses primarily on the
synergistic benefits as a means of assessing what premium over fair
market value the acquirer may offer for an acquisition.
We then focused our attention on the financial means through
which an acquisition is transacted,
and applied goal programming to
the problem of structuring the payment package according to the ac-
quirer's objectives for the consolidated companies' future performance.
The study proceeds with a survey of a number of computer programs designed to aid the decision-maker in performing the financial
analysis of a prospective merger. Our evaluation of these programs
led us to create our own program and to computerize the goal programming formulation previously developed to structure the payment
package. We conclude our thesis with a description and illustration
of the use of this program.
In perspective, the present work could be profitably com-
plemented or extended by further research in several areas. As
stated in the Introduction, we were unable to collect much data from
-256-
the field. To this extent, an attempt should be made to solicit cooperation from investment bankers, consulting houses and capital venture firms to establish which valuation methods are being employed
in practice.
Furthermore, some field research would probably allow the
addition of a number of real life cases, which are noticeably lacking
in this study. The availability of such examples would make a useful
contribution towards diffusing such techniques as probabilistic cash
flow analysis and adjusted present value among valuation practitioners.
Individual valuation techniques could also be improved.
For
instance, in the Adjusted P/E Technique, better ways of computing
the weights to be attached to each factor could be derived.
In the
goal programming application, more research needs to be carried out
in order to improve the way the user can specify the penalties to be
attached to deviations from his goals.
The framework of analysis that was presented is general
enoughto take both financial and operational synergistic benefits
into consideration.
In this thesis, we were mainly concerned with
the financial aspects of the acquisition.
We suggest further research
focus on the operational synergism which may result from a consolidation.
-257 Furthermore,
in the light of some of the research that is pre-
sently going on in the area of human resource management, factors
that were heretofore defined as intangibles may, in fact, turn out to
be quantifiable, and, therefore, amenable to explicit treatment in
valuation analysis.
More work needs to be channelled into extending the present
capabilities of FUSION as an aid to executive decision-making.
Addi-
tional modules should be designed to augment the program's functional
characteristics, so that ultimately, each step of the proposed framework of analysis may be carried out with the aid of the computer.
-258-
APPENDIX
A
Adjusted P/E Valuation Method
The problem addressed in this appendix is to value a firm by
submitting it to a direct comparison with other firms operating in the
same industry grouping. This comparative analysis serves to obtain
an adjusted P/E multiple to apply against an average past earnings
figure for the firm.
Although extremely subjective in nature, this line of thought is
followed by a large number of consultants, accountants, and bankers in
valuation studies .
The process requires the analyst to:
i.
Collect selected data of the firm and other firms operat-
ing in that industry and compute analysis figures.
ii.
Construct a hypothetical concern reflecting the averages
of the particular industry grouping.
iii.
Submit the firm and the hypothetical standard to a direct
comparison to determine the adjusted P/E.
iv.
Determine the firm's value by applying the adjusted P/E
to a representative earnings figure.
1 Especially
Especially in
in Europe.
Europe.
-259The description provided below is taken from an actual valuation
study performed by the Dutch firm of Pierson, Heldring and Pierson
(Amsterdam)2 . The process is rather rudimentary and accordingly,
wherever deemed necessary, we have suggested improvements. For
simplicity, it is assumed that the compilation of all pertinent data has
been performed.
An example of how we would implement the method
follows the descriptioni
We caution the reader not to view this valuation process, as having any theoretical value . The real benefits to be derived from it, stem
from the analysis of the firm and of its industry which need to be performed to determine the adjusted P/E.
Compute the Financial and Operating Performance Figures
Step 1:
to be Used
Of the many financial and operating ratios which can be compu-
ted for valuation analysis purposes, the following are used:
a.
Return on Investment (profitability)
b.
Profit Growth (potential)
c.
Profit Quality (predictability)
d.
Equity/Debt Ratio (solvency)
e.
Current Ratio (liquidity)
Each of these figures is computed as follows:
The name of the valuated company has been withheld by request
of its management.
3 The
method can be rendered more scientific if multi-correlation
or discriminant analysis is used to express the industry's P/E
as a function of the appropriate financial and operating performance indexes.
-260a.
Return on Investment
Actual: average profit of last three fiscal years in
percent of equity. Profit and equity are taken essentially as
reported by companies. Adjustments are made for nonrecurring and other items.
Proposed: time-weighted average of the last three
fiscal years' ROA (return on assets).
Use ROA instead of
ROE in order not to take the firm's capital structure twice
into consideration (i. e., here and in the solvency test). Timeweight
near-past
the ROA's so as to give more importance to the
over
the more distant one.
Compute ROA as:
ROA = Earnings before interest and taxes
Total assets
or as:
ROA = Before interest and tax profit margin * Asset turnover
where,
pretax and interest
Profit Margin = operating income
Sales
pretax and interest
+ nonoperating income
Sales
-26 1-
and
Asset Turnover =
b.
Sales
Total Assets
Growth
Actual: approximate absolute increase of net profit as
average over the last five fiscal years (on the basis of compound interest), i. e.,
=
Profit
(Year 5)
-1
Profit (Year 1)
Proposed:
annual compounded real growth rate provided
by reinvested net income.
Use the price indexes of base and
terminal year to determine deflated total percentage growth.
Profit Year 5
Profit Year 1
Profit Year 1
(Price Index Year 1
\Price Index Year 5
where,
ARE = change in Retained Earnings.
AEQ = change in total shareholder's
equity.
1 * ARE
xEQ
-262-
c.
Profit Quality
Actual: average percentage deviation of ROE from the
average of the highest and lowest ROE in the last five fiscal
years.
Proposed: coefficient of determination (r2 ) for the
logarithmic or linear (depends on the assumptions made about
growth) regression curve of the last five fiscal years' ROE. The
closer r2 is to 1, the more predictable the EPS of each year.
This method, although complicated, is basic to forecasting analysis.
If unable to implement this method, use variance of
ROE, i. e., the sum of the squared deviations of each year's
ROE to the average ROE of the last five fiscal years.
d.
Equity/ Debt Ratio
Actual: equity/loan capital.
Proposed:
compute solvency ratio as4
Shareholders' Equity + long-term debt
Shareholders Equity
e.
Current Ratio
Actual: current assets divided by current liabilities.
4
See Appendix B for explanation.
-263-
Proposed: same but adjusted if necessary5.
Construct Industry Averages
Step 2:
Once these indices have been computed for the firm, they have
to be compared to those pertaining to the industry.
To obtain the latter,
the analyst can consult financial information supplied by investment
companies, central bank research institutes or bureau of statistics.
Whenthe information is not publicly available, industry averages
may have to be computed using past financial statements of representative
companies in the industry.
5 At
any point in time, the current ratio may be distorted by sea-
sonal influences, slow-moving inventories or abnormal payment
of accounts payable just prior to the balance sheet date, etc.
The resulting current ratio CR' after a payment equaling x percent of total current liabilities is made,can be expressed
in terms of the current ratio CR before the payment is made as:
CR'
-
x
1 -x
and
dCR'
dx
1 - CR
(1 - x)
This means that a company for which CR < 1, can improve its
CR for balance sheet purposes by paying as much of its current
liabilities before the end of the fiscal year. The opposite holds
for a company with a CR > 1. No change when CR = 1.
-264Step
Determine the Adjusted P/E
3:
Actual: This is performed by selecting for each ratio a weight
wi and using the following equation:
P E1
PEf
ROEf
2
6
+
ROE.1
Gf
Gi
+
PQi
+
PQf
EDf
CRf
+ f
EDi
CR.
1
where
i = industry
f = firm
ROE = return on equity
growth
G = profit
PQ = profit quality
debt
ED = equity/long-term
CR = current ratio
PE = P/E ratio
Proposed:
According to our suggestions, PEf would be com-
puted similarly, but using our proposed variables, as:
PE
f
=
PE.
51
An
n= 1
CRf
a)o5
1
CRi.
1
ROAf
1
+~2
+ W2
ROA.
1
TAE.
Gf
G.1
1
+
(3
2
r.
4
TAEf
-265 where,
ROA = return on assets
r2
= coefficient of determination
TAE = Total Assets/Equity
con
Step 4:
= weight given
Determine the Firm's Value
In order to do this, it is necessary to compute an earnings figure which best represents the present potential of the firm. The des cribed technique suggests that the figure be calculated as the average
net profit over the last three fiscal years.
We propose that the figure be calculated as the time-weighted
average of the last three fiscal years. The time-weights should corres pond to those applied in Step 1 against the ROA's.
-266-
Example
Company XYZ
Major Financial Information ($000's)
1967
1968
1969
1970
1971
Sales
1,455
1. 684
2, 132
2,470
3,357
EBIT
57
95
140
167
155
Net Income
26
45
72
82
59
Current Assets
710
750
1,077
1,495
2,075
Total Assets
820
860
1, 187
1,695
2,565
Current
544
463
582
976
1,562
23
27
50
37
249
253
370
555
682
754
210
260
361
603
650
21
36
50
75
81
3. 92
5. 64
6. 56
6. 76
4. 62
Asset Turnover
1.77
1.96
1.80
1.46
1.30
ROA(%)
6.93
11.06
11.82
9.87
6.00
10.27
12. 16
13. 00
12. 02
7. 82
16.24
14.60
7.87
-3.20
. 172
.200
Liabilities
Long-Term
Debt
Stockholders'
Outstanding
Retained
Profit
Equity
Shares
Earnings
Maring
(%)
ROE(%)
Marginal ROE
growth rate (%)
EPS ($)
Leverage
Current
.124
(D+E)/E
Ratio
. 136
.090
1. 09
1. 07
1. 09
1. 05
1. 33
1. 30
1. 62
1. 85
1. 53
1. 32
-267 On the basis of this information, the adjusted P/E is determined
as follows:
1.
ROA
Time-weighted average ROA:
ROA
1
* 1.82 +
6
2.
2
9.87 + 3 *:- 6.00
=
8.26
6
6
Growth
a.
112. 3
Inflationary effect
109.
b.
Total Growth
59
=
1.03
1
= 226. 92 %
26
220.31 %
c.
Deflated Total Growth (b)/(a)
d.
Annual Compounded
e.
Change in Retained Earnings
f.
Change in Shareholder's
g.
Internal funds ratio (e)/(f) = . 1197
h.
Adjusted
Growth Rate (d) x (g) = 2. 048 %
Industry
= 10 %
Growth
= 17. 1 %
= 60
Equity = 501
-2683.
Profit Quality
a.
Linear Regression
of ROE
Trend Value
ROE
Year
x
2
x
Yt
y
(1)
(2)
(3)
(4)
(5)
1967
-2
4
10. 27
-20. 54
12. 786
1968
-1
1
12. 16
-12. 16
11. 920
1969
0
0
13.00
0
11. 054
1970
1
1
12.02
12. 02
10. 188
1971
2
4
7. 82
15. 64
9. 322
T otal
0
10
55.27
-8. 66
a
=
y
=
Y
55. 27
=
11.054
5
n
b
_CY
-8. 66
10
I
(x2
)
Regression Equation
yt = 11.054 - .866 * y
= . 866
(6)
b.
-269Coefficient of Determination
Year
Yt -
1967
- 1. 732
1968
.866
1969
y -y
Y
(yt -
-. 0784
2. 999
.750
1. 106
1. 946
0
)
(y
Y)
_
.0615
1. 223
3. 787
0
1970
. 866
.966
.750
.933
1971
1. 732
3. 234
2. 999
10. 459
7.498
16.464
Total
7. 498
2
r(
)
4. Solvenc
=
.455
16. 464
-
4.
Solvency
Long-term debt + Shareholder's Equity
Shareholder's Equity
Industry ratio:
5.
33%
Current Ratio
Current Assets
Current Liabilities
Industry's
ratio
-
2,075
1, 562
= 1. 49
= 1. 32
249 + 754
754
= 1. 33
-270-
6.
1
* $72
+
6
7.
+3
,
Time-Weighted Average Net Earnings
2
,
$82
6
$59 = $68.88
6
Adjusted P/E Computation
Industry
Firm X Standard
Ratio
Weight Product
1.
ROA
8. 26%
10. 00%
.826
.40
.33
2.
ROE Growth
2. 05%
10. 00%
.205
· 15
.03
3.
ROE Quality
. 455
.70
.65
.20
· 13
4.
Solvency
1. 33
1. 40
1. 05
· 15
· 16
5.
Liquidity
1. 33
1. 33
1.00
. 10
. 10
1.00
.75
Total
PEfirm
firm
. 75 * PEindustry
Value of firm ($000's)
=PE
fil
.75
9. 18 = 6. 885
* $68. 88 = $474. 240
-271APPENDIX B
Factors Affecting the P/E Ratio
This appendix considers those factors which most directly affect
the P/E ratio of a firm and thereby provides a rationale for the factors
which are considered by the Adjusted P/E Valuation Method.
1.
Earnings and Growth Rates
The prospect of future earnings per share (EPS) growth is the
obvious primary influence affecting the P/E multiplier.
The analysis
necessarily begins with historical data on the firm's earnings and past
growth rates and follows with the extrapolation into the future of the
relevant data. In doing so, it is vital to consider many factors including, but not limited to, the economic climate of the industry in which
the firm operates, and the health ability, vitality and age of management.
2.
Volatility of Earnings
Investors value minimum fluctuations from the anticipated earn-
ings trend line. In other words, lower risks are associated with stocks
which appear to promise lower per-share earnings volatility. Correspondingly, investors capitalize earnings at a higher P/ E when a low volatility
of earnings can be associated
with a particular
stock.
-2723.
Dividends
The effects of a firm's dividend policy on its stock price is a
much debated issue.
One school of thought holds that capital gains ex-
pected to result from earnings retention are more risky than are dividend expectations and that accordingly, the earnings of a firm with a
low payout ratio are capitalized at higher rates than are the earnings
of a high payout firm.
Another school of thought subscribes to the view
that any effect that dividends have on the price of a firm's stock is primarily related to information about expected future earnings conveyed
by a change of the firm's dividend policy. Recalling that corporate
managements dislike cutting dividends, this school asserts that a dividend increase favorably affects a stock's price by conveying to stock-
holders the idea that management expects the recent earnings increase
to be permanent. Many disagree with this assertion and argue that to
the extent that a low retention rate may be interpreted as meaning that
a firm is running out of internal investment opportunities, an increase
of the dividend payout ratio adversely affects a stock's price.
4.
Book Value Per Share
Book values are now generally considered to be of relatively
little value in determining a company's value, since they merely represent the historical investments that have been made in the company.
However, to the extent that the book value is an index of. the amount of
physical facilities available for production and, therefore,
of the poten-
tial future contributions that can be obtained under effective management,
it is a factor that affects the P/E multiplier.
-273-
5.
Capital Structure
The relative amounts of debt and equity used in a firm, or in
other words the leverage employed, is one of the main determinants
of the risk to which a firm and, therefore, its owners, are exposed.
If the firm earns more (less) on the borrowed funds, than it pays on
interest, the return to the owners is magnified (reduced).
Insofar as the utilization of leverage increases, the volatility
of earnings, the P/E multiple attributed by the market to a company's
stock may be adversely affected (i. e., increased).
6.
Liquidity
A firm's liquidity position is an indicator of its ability to meet
its maturing short-term obligations. The current ratio, that is, the
ratio of a firm's current assets to current liabilities, indicates the
extent to which the claims of short-term
creditors are covered by assets
that are expected to be converted to cash in a period roughly correspond-
ingly
to the maturity of the claims.
The quick ratio, or the ratio of current assets minus inventories
to current liabilities, is a stricter liquidity indicator since it measures
a firm's ability to pay off its short-term obligations without relying on
the sale of its inventories.
7.
-274Industry Group and Position of the Firm Within Its Group
Companies which participate in recognized growth markets are
apt to bright futures and will, therefore, receive recognition from investors by witnessing a high P/E ratio.
The absolute value of this
ratio will depend, however, on how the company compares with the
others within the same industry group. In performing the comparison,
investors usually examine such factors as have been already described
and evaluate them in the light of the published industry averages.
8.
Trading Features of the Stock
The liquidity of a stock, that is, the extent to which a stock can
be quickly sold, and the depth of the market in that particular stock,
that is, the extent to which the stock can be traded without affecting its
price, are important determinants of a stock's market price.
In general, the more liquid the stock and the deeper its market,
the higher the corresponding P/E ratio, all other factors being equal.
-275APPENDIX C
Determination of the Discount Rate: The Cost of Capital
The determination of the appropriate discount rate to be used
in any capital-budgeting context, has been a much debated issue and for
all practical purposes, there is no one single answer. Nevertheless,
some choices seem to be worse than others.
For instance, using past return on capital as the discount rate,
seems a poor criteria because a company with bad earnings would tend
to perpetuate past failures; a company with high earnings would forego profitable investments unless they returned the historic ratel.
Moreover, the argument is sometimes made that the cost of financing a project is the cost to service the package of securities that are
issued to pay for the transaction. This statement implies that the cutoff rate (i. e., the marginal cost of capital) at which projects are rejected, would depend on the particular structure of the package issued.
There seems to be a basic fallacy in this argument 2.Assume
that a firm has an after-tax cost of debt of 3 percent and that the after-
tax cost of equity is 10 percent. Further, assume that the firm is not
contemplating changing its long-term financial structure, that is, the
relative proportion of debt -to-equity.
Following the criterion above, if
1John F. Childs, "Profit Goals for Management," Financial
Executive, February 1964.
2J. F. Weston, E. F. Brigham, "Managerial Finance", Holt,
Rinehart and Winston, 1969.
-276the firm were to finance the next investment project with an all debt
package, the cut-off rate allowed would be 3 percent.
Conversely, if
the same investment were to be financed with an all equity issue, the
minimum cut -off rate applicable would be 10 percent.
The consequence of such a policy is that if through an all-debt
financing of a project yielding 3 percent, the firm exhausts its debt capacity, the cut-off rate for the next project will have to be 10 percent.
Hence, if a 9 percent project comes along, the firm would have to forego the opportunity to invest in it, although its yield is three times as
much as the last project.
This policy would clearly be non-optimal in
maximizing the returns to the stockholder.
The fallacy resides in the fact that one could not sell debt without having some common equity. In selling debt, one uses up some of the
debt capacity that the present level of equity provides. The "real" cost
of issuing debt, therefore, is the cost of servicing the interest plus an
extra amount that reflects the opportunity cost of the debt capacity which
is provided by a favorable debt-to-equity ratio. Similarly, the "real"
cost of issuing equity is, from an overall firm's point of view, the return demanded by the investors less the value of the additional debt
capacity that it provides.
The method that seems to be more widely recognized in theo-
retical circles, yet lends itself to practical applications, is the use of
the cost of capital.
If we take this view, it would seem that, under the
-277 -
assumption that permanent changes in the financial structure of the firm
are not contemplated, the cost of capital should be computed as the
weighted average of the cost of the individual securities,
total capitalization of the firm.
making up the
This should be used as the minimum
discount rate in evaluating projects of average risk relative to the
company.
This is in recognition
of the fact that while it is difficult to
raise capital in strictly the same proportions as the firm's financial
structure, over time most firms are able to finance in roughly a proportional manner.
That is, while a firm may finance with debt in one
instance and with common in another, over a period of time, it will
make sure that the relative proportions of outstanding debt and equity
remain constant and equal to a desired ratio.
In determining the firm's
cost of capital, one should look at the firm as a going concern: short-
term fluctuations are of little interest.
In practice, to compute the weighted average cost of capital,
one can use the "textbook" formula:
p = (1-
T)
i
D
D+E
+r
E
D+E
where
i = current average yield to maturity on the firm's bonds
r = expected rate of return on the firm's stock
-278D = market value of debt
E = market value of equity
Tc = corporate tax rate
p = hurdle rate
The assumptions that allow the use of the textbook formula are:
i.
The risk characteristics
of the investment under con-
sideration are similar to those of the firm's existing assets.
ii.
Adopting the investment cum financing does not change
the firm's debt-equity ratio.
iii.
The investment under consideration supports perpetual
debt (the project is long-lived).
In what follows, we will examine the relevant formulas to be used, when
the above assumptions no longer hold.
Case 1
Assumption
(i) does not hold
If the new investment is in a different operational risk class, one
can make use of the risk-equivalent cost of capital whereby the investment is financed in such a way as to keep the risk to the equity holders
constant. The risk-equivalent discount rate can be obtained from the
following formula:
-279D'
E'
D' + E'
D' + E'
I
p = (1 - Tc)i
where D'AD' + E) and E'/(D' + E) are the weights according to which
the investment must be financed if r is to remain unchanged. Tuttle
and Litzenberger make explicit the assumptions behind this technique
and provide a way to compute the weights. We cover their approach
in Appendix D.
Case 2
Assumptions
(i) and (ii) do not hold.
If by virtue of taking on the new investment, either the operating or the financial risk characteristics
of the firm change, then one
can use the Modiglianiand Miller 3 (M-M) formula:
P
=
Po 2 ( 1
Tc)
where
Po2= firm's cost of capital assuriAng all-equity financing
X = portion of debt used in financing the project
Case 3
Assumptions (ii) and (iii) do not hold.
When the leverage is changed and when the pro -
ject considered is of limited life, the M-M formula may still yield
3 Modigliani,
F. and Miller, M. H., "The Cost of Capital,
Corporate Finance and the Theory of Investments" The American
Economic Review, Vol. 48, No. 3, June 1958, pp. 261-97.
-280a correct answer.
But, in this case, it should be used with care and
recognizing the fact that it may lead to a wrong result.
It is at best a
rule of thumb.
In order to get around this limitation, Myers4 has proposed
the use of the Adjusted Present Value (APV) method as a practical
alternative to the analysis required by other cost of capital concepts.
In making use of this technique, one first discounts the after-tax,
before-interest
cash flows of the acquired firm as if it was equity financed.
The appropriate discount rate to be used in this case is Po2 . To the
present value of these cash flows, one then adds the present value of
the tax shield generated by taking on the additional amount of debt ADt
that the assets of the firm can support. The appropriate formula for
computing APV follows:
n
APV =
C
n
T
iDt
t
1 + Po2)
t=
(1 + i)t
This method, while mathematically more complex, is general
and will apply even to those cases where the M-M formula fails to give
the correct answer.
In order to determine Po2 ,one can use the follow-
ing rule of thumb:
S. C. Myers, On the Interactions of Corporate Financing and
Investment Decisions and the Weighted Average Cost of Capital, Alfred
P. -Sloan School of Management Working Paper 598-72, M. I. T.
-28 1-
1.
Calculate
p
= i(l -T)C x + r (1 -m)m
where
*
D
D
D
=
+ E
represents the market financial structure for the average firm
in that industry. r denotes the market required rate of return,
as discussed in Chapter II.
2.
Use the M-M formula to get to p02 using p*
P
P02
(1
-
T
)
This technique is applicable even if assumption (i) does not hold, as
long as an appropriate P02 is used.
Alternatively, p 02 may be obtained by equating the following two
equat ions:
V2
EBIT (1 - Tc )
+
I T
-c
i
-282 V2
-
EAIT
=
+
r
I_~~~~~{
i
This leads to the relationship:
(r - i) P0 2
EBIT
(r - P02 ) i
I
= times interest earned
from which P0 2 is determined to be:
(EBITl
\ I
i)
/) r - i/
1+(EBIT )( i
I
r -i
r
-283 APPENDIX
D
Risk-Equivalent Rate of Return
Tuttle and Litzenberger
have proposed a risk-equivalence
approach to render any investment project risk-equivalent to the assets
of the firm.
The procedure consists in compensating for any risk dif-
ferential by varying the amount of long term borrowing or lending.
This is equivalent to determining the method of financing2 which will
allow the firm to preserve the current degree of risk a 1 inherent to
its returns on equity 1t (denoted r in Section 1 of Chapter III). The
risk-equivalent return, which can be computed on this basis for the project, is then compared to the firm's weighted average cost of capital
P 1 to determine its acceptability or rejectability. The same approach
can be used to rank several projects according to their profitability.
Whenthe investment project consists of a prospective acquisition, the appropriate rate of return and risk to use are the acquisition's
rate of return on assets p2 and the standard error of returns a2 inherent to p.2 . The reasons for doing this stem from the fact that the acquirer will be able to modify the present capital structure of the seller
to suit his own objectives.
1D.
L. Tuttle and R. H. Litzenberger,
"Leverage,
Diversifi-
cation and Capital Market Effects on a Risk-Adjusted Budgeting
Framework", Journal of Finance (June 1968), pp. 427-443.
20Onlydebt and equity (including retained earnings) are considered as possible financing media.
-284The assumptions which need to be made in order to use the
suggested approach are:
The leverage of the acquirer is considered ideal for
i.
the risk 3 inherent in the present investment mix.
ii.
There exists a linear relationship between the firm's
expected return (i)
and estimate of standard error (i ) of
said rate of return.
iii.
A perfect market exists in the search for capital, i. e.,
the firm may borrow and lend at the same rate.
We shall return to these last two assumptions after the approach
is described.
Risk-Equivalent Rate of Return 4
In what follows, we determine the risk-equivalent rate of return
for a project and the financing ratio or mix of debt and equity which neu-
tralizes the risk effect of the project on the firm's return to equity.
Let,
2 = expected rate of return on assets from the project.
a2 = estimated standard error of the rate of return on assets
from the project.
3Risk is derived from the possibility that the firm's investments
might not return the desired yield, and is usually defined in terms of
the estimated standard error of returns a, i. e., as the square root of
the mean of the squared deviations of the realized annual returns from
the stream of projected returns.
4 The
ideas presented are those of Tuttle and Litzenberger,
op. cit. The presentation, however, is our own.
-285-
i = before tax lending/borrowing rate
T c = corporate tax rate
The rate of return on equity 2 and standard error of return
02 of any portfolio consisting of the acquisition candidate's assets and
some amount of lending or borrowing may be expressed as:
,*
E' + D'
1-
*
D'
'2
-i
E'
E'
E' + D'
02
E
E'
(1 - T
c)
(D. 1)
c
(D. 2)
2
where E' and D' represent the amounts of equity and debt to finance
the acquisition.
In order to neutralize the portfolio's risk, and, therefore, ensure that the acquirer's
cost of equity will not vary, we require that:
(D. 3)
02 = 01
Replacing a 2 by its expression
E' +D'
E'
al1
02
in (D. 2) yields:
(D. 4)
-286-
To the extent that the acquiring firm can also be viewed as a
portfolio of equity E1 and debt D 1, we may express
in terms of
the standard error of returns on assets al as
,
a1
=
Introducing
E+D
1
1
(D. 5)
(D. 5) into (D. 4) yields
E' + D'
E'
E 1 +D 1
E
1
(D.6)
(D. 6)
02
Since E' + D' represent the total value V2 of the acquisition
candidate, and, therefore, also equal the sum of the market value E 2
of its equity plus the market value D2 of any outstanding debt, we may
determine the financing mix to be:
El
E' + D'
a2
E 1
a1
E1 +D1
(D. 7)
D'
a2
E' + D'
a
1
E1
D'
E(D.
E 1+ D 1
=0~1
-
2
~ ~ 8)
-287-
These equations allow us to deduct the following conclusions:
i.
If a1 = 02, the acquisition should be financed in the
same mix as the acquirer's capital structure.
ii.
If o1 < 2, the acquisition should be financed with a
higher proportion of equity funds than the average investment
of the acquirer.
iii. If o1 > 02 , the acquisition should be financed with more
debt than the average
investment of the acquirer.
Furthermore,
if the acquirer is willing to assume the liabilities
of the acquisition, the purchase
PRICE2
price is:
= E' = E 2 + (D2 - D')
(D. 9)
From this equation, we deduct that if:
i.
D' < D2 , the acquirer will have to retire an amount
D 2 - D' of the acquisition's
ii.
long-term
debt D2.
D' = D2 the acquirer assumes all the acquisition's
liabilities.
iii.
D' > D2 , the acquisition provides an amount of debt
capacity equal to D' - D2 , which may allow the acquirer to
finance part of PRICE2 by issuing debt.
-288-
-
The risk-equivalent rate of return is simply obtained by introducing into (D. 1) the expressions for E' and D':
*1
2
E1+ D 1
= -
a2
-12
E1
E1 +D
i(1 -Tc
E1
a02
)
or
112
2=
1 p2
01 -
1i i (1 - T )
2
The following numerical example 5 illustrates how the procedure
is used for a case where a firm is confronted with the problem of screening four prospective acquisitions, all of which are independent and per-
fectly correlated with the firm's assets.
Each investment is described
by its expected rate of return L2and estimate of standard error of
returns
02. For the firm,
The after-tax
1 = . 15 and o1 = .30.
borrowing and lending interest rate i is 5 percent.
The risk-adjusted
rate of return is then computed as follows:
*
i
*12
Decision
. 30 .50
.05
.225
Accept
. 25
. 30 1.20
. 05
. 134
Reject
15
. 06
. 30 5.00
. 05
· 150
Indifferent
. 15
. 10
.30 3.00
. 05
.20
Accept
C ompany
~2
1
02
01
A
. 40
15
.60
B
. 12
15
C
. 07
D
. 10
-289Critique of the Assumptions
Thus far, we have described and provided examples of the potential uses of the risk-equivalence approach.
We recall that at the
outset of the description, assumptions were made (i) as to the shape
of the risk-return trade-off curve of the firm, and (ii) as to existence
of a perfect market for the search of capital.
Let us now examine
how limiting such assumptions really are. For that purpose, it is useful to make use of risk-return
graphs.
The first assumption made states that the relationship between
the firm's risk and return is linear (line if). We know, however, that
a risk-adverse
company requires a geometric rather than an arith-
metic increase in the rate of return () as risk (a) increases.
fore, the relationship between
There-
and o can be represented by curve im.
According to this curve, (i) the firm would be indifferent in undertaking
any one of two or more companies requiring an equal outlay of equity
funds and having a risk-return
combination on curve im; (ii) the firm
would accept any company whose risk-return
GC
1
I
Figure D-1
Figure D-1
combination is under the
-290curve; and (iii) the firm would reject any acquisition candidate dis playing a risk-return
combination above curve im.
Under the light of this discrepancy, the model fails to provide
an adequate risk-equivalent rate of return in only one case, namely;
where the company under consideration has a risk-return
combina-
tion lying inside the shaded area of Figure D-1. As Figure D-2 shows,
the risk-equivalent rate of return *2 of a portfolio consisting of any
such investment project (point P 2 ) and a certain amount of borrowing4
is inferior to
,,
1.
Company 2 is, therefore, classified as rejectable.
This counters the criterion provided by curve im. In fact, the acceptance of company 2 would lead to a decrease
cost of
of the acquirer's
equity, and hence to an increase in its market stock price.
AT
V
04
Ur2
4
Figure D-2
4
Because a2 < 1' in order to render Company 2 as risky as
the assets of the acquirer it is necessary to finance it mainly by borrowed funds.
-291The second assumption states that the lending and borrowing
rates are equal. This is not always true.
We know that depending on
the firm's capital structure and the amount of funds needed to be borrowed (to mention only a few factors), the borrowing rate iB may be
higher than the lending rate iL. The introduction of these two rates
into the model results in the model's risk-return trade-off curve becoming a broken line, as i B Pf. This in turn, hampers still further
the accuracy of the model as a project selection technique because the
shaded area becomes larger (Figure D-3). Therefore, the second
although seldom true, is, in fact, beneficial
assumption (i. e., iB = iL),
to the accuracy of the risk-equivalence approach.
U
4
4
I
I
I
I
I
I
I
I
I
L
Figure
D-3
Figure D-3
-292 -
In conclusion, we can state that the assumptions made by Tuttle
and Litzenberger are not overly binding. The approach lends itself
usefully to the problem of determining the mix of equity and debt to be
used in financing an acquisition whose risk profile differs from that of
the acquirer.
-293 APPENDIX E
Alphabetical List of Acronyms Used
ATBIR
= After-tax-bond-interest -rate
B(t)
= Oustanding amounts of bonds at the end of year t
BCR
= Bond conversion rate (no. shares per $100), if any
BIR
= Bond -interest -rate
BVi
= Book value of assets of company i
Ci(t)
= Cash balance of company i at the end of year t
CP(t)
= Oustanding amount of convertible preferred at end of year t
CPCR
= Convertible preferred conversion rate (no. shares per $ 100)
CPD
= Convertible preferred divident yield
CSI
= Common stock issued
D.(t)
= Amount of long-term
DER
= Debt-to-equity ratio
DIV
= Projected
DPSi(t)
= Divident-per-share
Ei(t)
= Net-earnings of company i during year t
EPSi(t)
= Earnings -per-share
EPSI(t)
= Earnings-per-share of company i for year t
EQi(t)
= Amount of equity of company i at end of year t
MINOWN
= Minimum ownership required (%)
NOSi1
= Number of outstanding shares of company i
debt of company i at tl
DPS for company 1
of company i for year t
of company i for year t
end of year t
-294-
P.
= Stock price of company i, per share, prior to acquisition
PAYOUT(t)
= Company 1 dividend payout ratio for year t
PAY02
= Payout ratio for company 2
PE.
= Price -earnings multiple of company i
PRICE2
= Price to be paid for the acquisition
Si(t)
= Sales of company i during year t
SFR
= Sinking fund requirement (% of initial issue)
TAXR
= Corporate
t
=
p
tax rate
Initialyear for sinking fund
payments
Vi
= Value of company i
WCi(t)
1
= Net-working-capital balance at the end of year t
-295APPENDIX F
The QUICKSCAN II Program
This appendix presents the program listing (FORTRAN IV)
and a few sample output pages of our own version of QUICKSCAN
(presented in Section B. 2 of Chapter VIII). The data used is the same
as that used for the sample run of FUSION.
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-304APPENDIX
G
A Sample Session Using FUSION
In what follows, we present a sample session using FUSION.
Insofar as the questions are self-explanatory,
on them.
we shall not comment
User's responses are typed on the line following each ques-
tion.
As may be observed, the user may, before inputting any
required information, type "list" or simply "1" to have the program
display the values that had been used in the previous run. If he wishes
to reuse the same values, he must simply type a slash (/).
If he
wishes to insert his comments in between any input vales, he can do
so by typing a semicolon, inserting his comments, and continuing to
enter data in the next line. These comments become clear in the
following pages.
To avoid many of the problems we encountered initially with
the package determinator subroutine, we recommend the user first
use the program by specifying the proportions of securities to be used
in the package. The results thus obtained will provide him with the
insight of possible values that the various variables may assume and
which is required to efficiently use the package determinator subroutine.
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-345 BIBLIOGRAPHY
Books
1.
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2.
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1.
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Gillette, C. G., "How Buyer and Seller Look at a Merger",
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Mergers"', Journal
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-349-
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